5

Problem #5: Consider the following function. f(x,y) [Cy + 4) Inx] - xe4y ~xly - 6)4(a) Find f,(1,0) _ (b) Find f,(1,0) _Problem #S(a):Problem #5(b):...

Question

Problem #5: Consider the following function. f(x,y) [Cy + 4) Inx] - xe4y ~xly - 6)4(a) Find f,(1,0) _ (b) Find f,(1,0) _Problem #S(a):Problem #5(b):

Problem #5: Consider the following function. f(x,y) [Cy + 4) Inx] - xe4y ~xly - 6)4 (a) Find f,(1,0) _ (b) Find f,(1,0) _ Problem #S(a): Problem #5(b):



Answers

Differentiate the functions in Problems $1-28 .$ Assume that $A$ $B,$ and $C$ are constants. $$y=5 \cdot 5^{t}+6 \cdot 6^{t}$$

Okay, This question wants us to find the derivative of why So do I. D. X is just the derivative with respect to X of our function here. And then to simplify, this will just distribute the derivative to each term. So this is the derivative of five times two to the ex, plus the derivative of negative five X plus, the derivative of four. And then for our first term here, we're just gonna have to use the fact that the derivative of age, the X is just eight of the ex times, the natural log of the base. So then we can plug in here for that formula. So the five stays out in front and the derivative to do the X is to to the ex times, the Ellen of two. And then for other terms, we could just use the power roll so derivative of negative five X is just negative five and then the derivative of four is just zero. So this is our final answer for

Okay here we get given a function. That function is F of X equals six. Either the four X over two X plus three. We want the linear ization of this function at a equals zero. So for linear ization we need two things. We need this point and a slope. We'll start off with the point the X coordinate. The point is given to us zero. We need to find the like coordinate. So we're going to compute F of zero. Just six ft of the zero of the zero plus three. Should give us 6/3. Just to coordinate is zero comma. Two will hold on to that later. Okay, now we need the slope so we need the derivative for that. So after kind of X. This will be another closer role. We'll set up on the division symbol, the denominator times the derivative of the numerator. There is the numerator will be 24. Either the four X minus the numerator times the derivative of the denominator all over the denominator square. Okay. We could spend time simplifying this but we don't really need to we just need to evaluate this at our A value so we evaluate it at a equals zero. Okay, I'll skip some of the calculations here. So give us three times 24 ft of the zero minus six times E. To the zero times two. All over two times 00 plus three. It's three squared mm. Little bit more simplification here. 24 times three. We'll have 72 minus 12/9. Should give us 60 of the nine which will simplify to 20/3. Okay. And this is our slope. So how do we put the linear ization together? We use point slope form I minus Y. One equals M. It's x minus X. One. We've got to point up the top and a slope that we've just found substitute these in quick little bit of rearranging can get us to the answer. We'll see in the back of the book, which is why you cause 20/3 X plus two. Just move into two over and distributing the 20/3. And that's it.

For this problem we are finding functions F and G. So that the comm positive F. And G together is equal to H. So what that means is because the composite of F and G. Is F of G of X. That means I'm trying to find the ffx and the G. Of X function so that when I do the composites together, their end result is two X plus three all to the fourth power. So what I like to do for problems like this is think of it in terms of inner and outer. So within this function I have an inner and outer function. So when there's parentheses involved, the inner function is always can always be whatever is inside of the parentheses. So then if I look at it in terms of okay, well if that's taken care of then what's left would be this to the fourth power. So I can say that that becomes my outer function just that X. To the fourth. So then if I need to match those up with Fx and Gx. So because I have F. Of G. Of X. And that means I want my G. Of X to be my inner function. So that would be two X plus three. Whereas my ffx would be my outer function X. To the fourth. So if I go through and check that I'm gonna check to make sure if I do the composite I would get two X. Plus three to the fourth power. So if I do F. Of G. Of X. That means F. Of X. Is my outer function X. To the fourth is outer G. Fx's inner. So that's gonna be F. Of two X plus three. So that means every time I see an X. In my F. Of X. Function I'm gonna plug in my entire G. Of X. Function which is two X plus three. So that would indeed get me two x. plus three To the 4th power which is H. So these are possible answers for this question.

Okay. This question wants us to find the derivative of y with respect to t. So writing that out, we see that Do I d. T is just the derivative with respect to t of our entire function. Why? And then we can break up this derivative by distributing its each term. So we get the derivative with respect to t of our first term, plus the derivative with respect to t of our second term. So for our first term, we can just use the power rule. So bring down that too. And then we multiply that by the five in front we get 10 t plus four times the derivative of eternity, which we know from our identity that the derivative of eat of the tea is just itself. So four feet of the teeth ends. This is our final answer for the derivative


Similar Solved Questions

5 answers
Y(d) Find the polnts general 2y solution 1 of the 402 given differentlal equatlon
y(d) Find the polnts general 2y solution 1 of the 402 given differentlal equatlon...
5 answers
26 Usc tke &lgoitkuu W sociion 2.2 t0 iud A-14 = =3
26 Usc tke &lgoitkuu W sociion 2.2 t0 iud A-1 4 = =3...
5 answers
I6ni15 points) Isoleucine is one of the 20 commonly ionization constants of Ka, 4.81 occurring amino acids with acid predominant x10 3, and Kaz 1.75 x 10-10. Determine the form of isoleucine acid and draw its structure properly protonation of each acidiclbasic site indicating the state CH(CHJ)CHZCH:) The substituent (R group"') for isoleucine isat pH = 7.40 at pH = 12.00
i6ni15 points) Isoleucine is one of the 20 commonly ionization constants of Ka, 4.81 occurring amino acids with acid predominant x10 3, and Kaz 1.75 x 10-10. Determine the form of isoleucine acid and draw its structure properly protonation of each acidiclbasic site indicating the state CH(CHJ)CHZCH:...
5 answers
15 marks Determine whether the following improper integrals are converg- ing or diverging, and if they are converging calculate them. [5 marks each](a) Jo (r+1)dx (b) fi O0 6dx f xe 1dx O0
15 marks Determine whether the following improper integrals are converg- ing or diverging, and if they are converging calculate them. [5 marks each] (a) Jo (r+1)dx (b) fi O0 6dx f xe 1dx O0...
5 answers
Item 9Part AHow much current is flowing in wire 4.75 I long the maximum force on it is 0.675 N when placed in uniform 0.0800-T field?Express your answer t0 three significant flIgures and Include the appropriate units_ValueSubmitRequest Answer
Item 9 Part A How much current is flowing in wire 4.75 I long the maximum force on it is 0.675 N when placed in uniform 0.0800-T field? Express your answer t0 three significant flIgures and Include the appropriate units_ Value Submit Request Answer...
3 answers
5) Let D = {a + b0 + c02 @,b,c € Z} where 0 satisfies the equation 03 + 0 _ 1 = 0 Show that D is an integral domain and 0 is a unit in D_ What is 0-1
5) Let D = {a + b0 + c02 @,b,c € Z} where 0 satisfies the equation 03 + 0 _ 1 = 0 Show that D is an integral domain and 0 is a unit in D_ What is 0-1...
5 answers
DetAILSLARATIO 4.1.006. Qv4 SubmnissIon: UscdNOTES45k YQUR TEACHEPFill in the blanks The chord joining the vertices of an ellipse Is called the Its midpoint is the of the ellipseandNeed Helo?Show My Work (Ootlonall @DETAILSLRRAT1O 4 3.011, 0/4 Submisslons UsedMY NOTESASK YOUR TEACHERMatch the equation with its graph.
DetAILS LARATIO 4.1.006. Qv4 SubmnissIon: Uscd NOTES 45k YQUR TEACHEP Fill in the blanks The chord joining the vertices of an ellipse Is called the Its midpoint is the of the ellipse and Need Helo? Show My Work (Ootlonall @ DETAILS LRRAT1O 4 3.011, 0/4 Submisslons Used MY NOTES ASK YOUR TEACHER Matc...
2 answers
Y' 1Oy' + 9y =0 y"' - 2y' - Jy=ety(0) = 2 y(0) = 20 y(0) =y(0) = 0
y' 1Oy' + 9y =0 y"' - 2y' - Jy=et y(0) = 2 y(0) = 20 y(0) =y(0) = 0...
5 answers
[25 points] Consider the following three samples of some function f:index kf(Ea)18Produce the equations required to compute the spline s(.) consisting of two quadratic funetions, and $2 and define in terIs of them IE necessary; use the endpoint condition $ (To) = 0. Solve for the coefficients of the two quadratic functins that form the spline_
[25 points] Consider the following three samples of some function f: index k f(Ea) 18 Produce the equations required to compute the spline s(.) consisting of two quadratic funetions, and $2 and define in terIs of them IE necessary; use the endpoint condition $ (To) = 0. Solve for the coefficients of...
5 answers
Point) Suppose zsin Y, x =382 + 1/2 ,y =-6st .A. Use the chain rule to find and Jz as functions of X, Y, $ and t % dB. Find the numerical values of and when (s,t) = (2,3). 9(2,3) = d7 (2,3)
point) Suppose z sin Y, x =382 + 1/2 ,y =-6st . A. Use the chain rule to find and Jz as functions of X, Y, $ and t % d B. Find the numerical values of and when (s,t) = (2,3). 9(2,3) = d7 (2,3)...
1 answers
In Exercises $17-20,$ sketch the graph of $y=x^{n}$ and each transformation. $$ \begin{array}{l}{y=x^{3}} \\ {\text { (a) } f(x)=(x-4)^{3} \quad \text { (b) } f(x)=x^{3}-4} \\ {\begin{array}{ll}{\text { (c) } f(x)=-\frac{1}{4} x^{3}} & {\text { (d) } f(x)=(x-4)^{3}-4}\end{array}}\end{array} $$
In Exercises $17-20,$ sketch the graph of $y=x^{n}$ and each transformation. $$ \begin{array}{l}{y=x^{3}} \\ {\text { (a) } f(x)=(x-4)^{3} \quad \text { (b) } f(x)=x^{3}-4} \\ {\begin{array}{ll}{\text { (c) } f(x)=-\frac{1}{4} x^{3}} & {\text { (d) } f(x)=(x-4)^{3}-4}\end{array}}\end{array} $...
5 answers
The planet Mars has an orbital radius about the sun of 2.28e11 mand completes an orbit every 687 days. What is the average speed ofMars relative to the sun in miles per second?
The planet Mars has an orbital radius about the sun of 2.28e11 m and completes an orbit every 687 days. What is the average speed of Mars relative to the sun in miles per second?...
3 answers
At last, this problem culminates with YOu showing that, given the Field and Order Axioms_ the multiplicative identity must be greater than the addlitive idlentity 0. That is, prove: 1 > 0.
At last, this problem culminates with YOu showing that, given the Field and Order Axioms_ the multiplicative identity must be greater than the addlitive idlentity 0. That is, prove: 1 > 0....
5 answers
14 28 series 7 -56 2756 274)4) Find anb) Determine whether the series is convergent or divergent c) Find the sum of the series
14 28 series 7 - 56 27 56 27 4) 4) Find an b) Determine whether the series is convergent or divergent c) Find the sum of the series...
5 answers
1. (a) Write out the partial fraction decomposition of the function f(x) = (Remember to x3+x first factor the denominator:)(b) Solve for the unknowns from part (a):(c) Evaluate the integral dx x3tx
1. (a) Write out the partial fraction decomposition of the function f(x) = (Remember to x3+x first factor the denominator:) (b) Solve for the unknowns from part (a): (c) Evaluate the integral dx x3tx...
5 answers
Question 5 (2 points)lSuppose f(w) dr| -4 / f(r) dr 5 I12 and 761 f(r) d. 154Calculatef(e) [email protected]
Question 5 (2 points)l Suppose f(w) dr| -4 / f(r) dr 5 I12 and 761 f(r) d. 154 Calculate f(e) dr 0-8 09 @8 WND613...

-- 0.025296--