5

Flr_D)_flv) to find the following derivative ITsc (llc limit definition Iiwy 2 (5 m ot M R r? 9...

Question

Flr_D)_flv) to find the following derivative ITsc (llc limit definition Iiwy 2 (5 m ot M R r? 9

flr_D)_flv) to find the following derivative ITsc (llc limit definition Iiwy 2 (5 m ot M R r? 9



Answers

Find the derivative of each function by using the quotient rule. $$R=\frac{5 i+9}{6 i+3}$$

Here we have a function that's a quotient. So in finding the derivative, we're going to use the quotient rule. And in the sun, inside of the quotient, we have some composite functions, so we'll be using the chain rule as we go. So h prime of our would be according to the quotient rule. We have the bottom to r plus one to the fifth times the derivative of the top. So here we're going to stop and use the chain rule. We bring down the three and we take our squared minus one to the second. And then we multiply by the derivative of the inside, which would be to our so So far, we have the bottom times, a derivative of the top. Now we need minus the top minus R squared minus one, cubed times the derivative of the bottom on the derivative of the bottom. We're going to need to use the chain rule. So bring down the five and raised to R plus one to the fourth and then multiply by the derivative of the inside, which is to and that's all over the bottom squared. So that's all over to R plus one to the 10th. Okay, The rest of it is all about simplifying. What are we going to do to simplify this? So let's look at this whole first part as the first term and this whole second part as the second term. And let's see if they have anything in common that we can factor out. So they both have a factor of two. They both have a factor of to R plus one to the fourth. This one has an extra that we're going to leave behind. And this one has a two r plus one to the fourth. So let's factor that out. And they both have a factor of R squared minus one squared. The 2nd 1 has an extra that we're going to leave behind. It will factor R squared minus one squared. Now, what did we leave behind? So in the first part, we left one of the two our plus ones and we left the three and the are So we have three are times a quantity to R plus one. What did we leave behind in the 2nd 1? Well, we still have the minus, and then we have one of the R squared, minus ones that was left behind. And we have the five. So we have minus five times R squared minus one. Okay. And that's all over to R plus one to the tent. So what we can do now is reduce our to our plus one to the fourth over to R plus one to the 10th. And that would just leave us with two r plus one to the sixth on the bottom. And then the next thing we can do is distribute and simplify this quantity on the brackets. Okay, We're going to grab a little extra space to simplify the quantity in the brackets. So we'll distribute. The three are and we get six r squared plus three are and we'll distribute the minus five when we get minus five r squared plus five and will combine like terms. And we have our squared plus three are plus five. Okay, so let's put that back into our answer. So we have two times R squared minus one squared times are squared plus three R plus five. That quantity. We just simplified over to R plus one to the sixth

So what we want to do here is we're wanting to find the derivative of x squared minus five using the definition of the derivative which I have provided here. Okay, so let's just get down to it. So we're going to have the limit As Delta X approaches zero of F of X plus delta X. Well, that means that anywhere I see an X in F of X instead, I'm going to put an X plus delta X. Okay, And so that's going to be X. Sorry about that. X plus delta X squared -5. And then I'm going to subtract affects. Well, what is F of X? That is X squared minus five. And all of that is going to be divided by delta X. So what does that equal? Well, we want to expand this X plus delta X. So that gives the limit As Delta X Approaches zero. And because it's square really, that means X plus delta X times X plus delta X minus five minus x squared minus five. And of course all that is still being divided by delta X. They put the equal sign over here and next we're going to use the foil method. Okay, first Outer, in our last first Outer, in our last two multiply that out. That's going to give us the limit as delta X approaches zero. Don't forget your limit of X squared um Plus X times delta X plus X times delta X plus delta X square. Okay minus five minus X squared minus five. Okay. And all of that is still being divided by delta X. So let me see if I could scroll down a little bit scroll down a little too much. That's okay. Very good. That's good. Okay and so what that ends up being is the limit As Delta X approaches zero of X squared plus two x times delta x plus delta X squared -5. And now I'm going to actually distribute this negative across here. And that's gonna give us minus X squared plus five. And of course all of that. Oops sorry about that. All of that is still being divided by delta X. Okay and that gives us the limit As Delta X Approaches zero. Um and so some things are going to cancel out here. I have an X squared and a negative X squared. So those cancel out, I have a negative five and a plus five. So those cancel out. And so what I end up having is to X delta ax plus delta X squared, still divided by delta X. And so what I wanna do is I want a factor um that delta except top so I can divide it by this delta X. And the denominator. And so I'm going to do that. So I still have the limit as delta X approaches zero. And I'm going to factor out a delta X to get two X plus delta X. And that is still being divided by delta X. But not for long. Because now these DELTA X's cancel out. And I'm left with the limit As Delta X approaches zero of two X plus delta X. And now I can finally um insert my limit. And so the limit goes to zero of delta X, which gives me two X. And that is the derivative.

For the following problem, let's calculate the derivative. So it's gonna be F of X. Yeah, equals nine X. of the 5/2 -2. Yeah. Yeah. Um And this is going to be divided by X. So what we're gonna do is calculate the derivative. Um and that's going to be through using the quotient rule. So it's going to be the low times the derivative of the high frequency is going to be five halves times nine, so it's gonna be 45 over to X to the three house um minus this term here, Times the derivative of the bottom, which we know is just going to be one all this divided by X squared. And we can confirm this by looking at f prime of X and end up being the exact same as we see here.

Hi there. In this problem, we were asked to differentiate this equation X cubed times are to the fifth equals one. And we were asked to calculate the derivative with respect to X. And so we'll have to take the derivative with respect to X. We'll just take the derivative of both sides of the equation like we always do and keep in mind as we go that are really it's a function of X. We could think of it as our backs were supposed to assume that for this, um, for this particular problem and we'll be done right when we have figured out what d r d X is or if you prefer our prime, they mean the same thing. So we want to get that by itself. Okay, so start with the left side, the derivative of X Cube out of the fifth. We will need the product rule because we have X cubed times out of the fifth. So let's use the product rule will have executed times. The derivative of this second factors the derivative art of Fifth Plus. Now that derivatives of the first thing, they're derivative of X cubed time. Start of the food. That is just the product rule coming from the left side equals. Now, over here on the right, the derivative of the constant one is zero. Okay, let's calculate these derivatives now. So X cube is just x cubed the derivative art of the fifth. Well, you have five art of the fourth just using the power rule. But because our is a function of X lead two multiplied by D r d x are just playing the role that why usually plays in a lot of these problems. I mean, if you wanted to, you could also call that our prime instead of r d r D x. Either way. Okay, we're here. The derivative of X Cube is three x squared, and that art of the fifth stays the same. Okay, so we're almost done. Remember, our goal was to get this is the RDX by itself. So here it is. We just need to do a little elder brother. Get it by itself. Let's start by subtracting this other term from both sides. So that will give us. Let's see, we can rewrite this 1st 1 a little better as well. So let's bring the five out in front your extra The third part of the fourth, the RDX on the right side, we have negative three X squared R Okay, And then we can see how it end. Finally, we will just divide both sides by five. Execute are the fourth. Okay, so that means we have the RDX by itself now. And can we simplify it all a little bit? So we have negative three on top five on bottom X squared over X. The third will give us an X in the denominator and art of the fifth over. Art of the fourth will give us art of the first in the numerator and we are done. Hopefully that helped.


Similar Solved Questions

5 answers
UW6O_CHLAB121_API_20180502_014.tdExpt :Sim:Block:H. Exp:vertical scale 8.668E-05PPM12.511.510.59.58.57.56.55.54.53.52.51.50.50.5
UW6O_CHLAB121_API_20180502_014.td Expt : Sim: Block: H. Exp: vertical scale 8.668E-05 PPM 12.5 11.5 10.5 9.5 8.5 7.5 6.5 5.5 4.5 3.5 2.5 1.5 0.5 0.5...
5 answers
Solve for the verucal and horizontal componenty o( the reactions at and B Member BC I5 4 Hforce member;0SCEETR
Solve for the verucal and horizontal componenty o( the reactions at and B Member BC I5 4 Hforce member; 0 SCEETR...
5 answers
F()= x+1Sx" sinx on ie B. Find the average value of the function_ interval - I,z]:fae =0 fae 77 fa 21 fav 2 21 None of the above
f()= x+1Sx" sinx on ie B. Find the average value of the function_ interval - I,z]: fae =0 fae 77 fa 21 fav 2 21 None of the above...
5 answers
Points) Determine whether the following set form subspace in R' (T1,T2,T3,T4) such that €1 T4 = 0, I1 | T2 | I3 - I4 = 0}
points) Determine whether the following set form subspace in R' (T1,T2,T3,T4) such that €1 T4 = 0, I1 | T2 | I3 - I4 = 0}...
5 answers
Find the volumie of the tetrnhedron houncexl by the coordinate plancs and the plane c/a +v/b + -/c 0,6,€
Find the volumie of the tetrnhedron houncexl by the coordinate plancs and the plane c/a +v/b + -/c 0,6,€...
5 answers
Q1/ Explain the Effective Atomic Number Rule forthe following complexes: [Mn(CsHs) (COJa] Na[Co(Co)-] [Cr(COJs(CzH4)]
Q1/ Explain the Effective Atomic Number Rule forthe following complexes: [Mn(CsHs) (COJa] Na[Co(Co)-] [Cr(COJs(CzH4)]...
5 answers
For Exercises $5-18,$ solve Exercises $41-54$ respectively, from Section 3.1
For Exercises $5-18,$ solve Exercises $41-54$ respectively, from Section 3.1...
5 answers
Attach File (9 Fena QUESTION (9)+ inscribed the ()+ 5 the dimension the last 1 of three ellipsoid the digits grec @fyouar drorir Conten{ Ccrclo xoq QUID maximum volume that can
Attach File (9 Fena QUESTION (9)+ inscribed the ()+ 5 the dimension the last 1 of three ellipsoid the digits grec @fyouar drorir Conten{ Ccrclo xoq QUID maximum volume that can...
5 answers
Verify that the given fiuctions (Y1 and Yz) form the fundamental set of solutions of the given ODE Then solve the given initial-value problemxy" Txy' 15y = 0J1 = x3 .JYz = x5 y(1) = 0.4. y(1) = 1 Hint: assume the given ODE has a solution of the type y = xm Then. derive an auxiliary equation and solve as usual. This type of ODE is named an Euler-Cauchy ODE
Verify that the given fiuctions (Y1 and Yz) form the fundamental set of solutions of the given ODE Then solve the given initial-value problem xy" Txy' 15y = 0 J1 = x3 .JYz = x5 y(1) = 0.4. y(1) = 1 Hint: assume the given ODE has a solution of the type y = xm Then. derive an auxiliary equa...
5 answers
A pebble is dropped from hot-air balloon and the distance at which it has fallen is given by the function s(t) 16t2_ where t is in seconds. and $ is in feet.How fast Is the pebble falling after 1.5 seconds? Give correct units with your aswer.What is the pebble's acceleration after 1.5 is in feet Give correct umits with your answer:
A pebble is dropped from hot-air balloon and the distance at which it has fallen is given by the function s(t) 16t2_ where t is in seconds. and $ is in feet. How fast Is the pebble falling after 1.5 seconds? Give correct units with your aswer. What is the pebble's acceleration after 1.5 is in f...
5 answers
Ledrenaadab< Dateinl-0PCNTSFDPRECALCS 4.7.015Uctrily , - C7ttnaTannMaun 1cos 2 =
Ledrenaadab< Dateinl -0PCNTS FDPRECALCS 4.7.015 Uctrily , - C7ttna Tann Maun 1 cos 2 =...
5 answers
Use trig ratios to find Angle A in the cuboid belowWhat is the length of y in the cuboid?
Use trig ratios to find Angle A in the cuboid below What is the length of y in the cuboid?...
5 answers
QUESTION 3Explain the following theorems in your own words and state two applications of each theorem in chemical engineeringDivergence theorem Stokes' theorem
QUESTION 3 Explain the following theorems in your own words and state two applications of each theorem in chemical engineering Divergence theorem Stokes' theorem...

-- 0.064986--