5

QUESTION 14Usc the chain rulc to find=tan (2-Sy),x=5= cost, J = e' Int~xx $ sint 1+(rl_ Sy ~252 cost" Sint -1+(s2-cos?t- 8e' -Int}2x $ COS?_cos-11+...

Question

QUESTION 14Usc the chain rulc to find=tan (2-Sy),x=5= cost, J = e' Int~xx $ sint 1+(rl_ Sy ~252 cost" Sint -1+(s2-cos?t- 8e' -Int}2x $ COS?_cos-11+(s2-cos?t- 8e' -Int}

QUESTION 14 Usc the chain rulc to find =tan (2-Sy),x=5= cost, J = e' Int ~xx $ sint 1+(rl_ Sy ~252 cost" Sint - 1+(s2-cos?t- 8e' -Int} 2x $ COS?_ cos-1 1+(s2-cos?t- 8e' -Int}



Answers

Cost Find the cost function for each marginal cost function.
$$
C^{\prime}(x)=x^{1 / 2} ; \quad 16 \text { units } \operatorname{cost} \$ 45
$$

In this problem we wish to find the derivative of perspective T. Using chain roll, one of P equals X squared Y. Z. To find parametric lee with X equals 70 Y equals coast T and Z equals E. To the T. This question challenge the understanding of multi very differentiation. In order to solve, we must understand chain rules daily Chairul one which states that DP DT is D p D f D f c T. Maybe you are you all ready to go see PVC DZ DT. So to song we must find a six year old is given in the DPT formula for this we have DPD X equals two. X. Y. Z. G. P G Y equals X squared C. And D P D equals X squared Y. Next differentiating X. Y. And Z. With respect to T. Gives DF DT equals coast T D Y equals negative sci fi nd DDT even the T. Thus plugging in X. Y. Z into our three P departures, relatives and plugging into GPT gives to scientific oh square T V. The t minus sine, Q T V. The T plus Science square T Coast T V. The TT

Okay, so we're given a marginal cost function, and that's the root of our of our cost function and were also given that two units costs $9.44. So that is CFL alluded to is equal to 9.44 and rash to find our, um, cost function well, we could just use this derivative take the integral to get cfx. So it's not right doing that. That's the integral of 1.2 x. A lot of 1.2 he x notice that we have a constant there. We can pull out using a constant multiple rule. Okay, I know. Let's take our integral of this exponential function. So that gives us Ellen of 1.2 times 1.22 of R of X over, um, Ellen of 1.2. So these two council and we're left with this plus Kate, that is a constant function or not a constant function. Our cost function is equal to 1.2 x plus cape, and now let's plug in, see, evaluated up two is equal to 9.44 to find kit. So we have 9.44 is equal to one point shoes to part two less cake. So one point to the bar to is 1.44 subtracting 1.44 on both sides. We get that K is equal to eight. So our cost function here we replaced RK with the eighths is falling.

I think they were given the fall that are marginal cost function. Well, that's equal to the falling. And we're also given that eight units costs $58. That is our cost function evaluated. Its is equal to 50 eight's okay and were asked to find our cost function. So we're given the derivative or cost function so we can take the girl of see Prime of X, and that would be equal to our cost function. So let's start by doing that, that's X across to over three plus two the X Using our some rule, we get the fulling okay, and then we can pull out our constant Did I gives us a falling. Okay, I know. Let's use our power rule. So we get extra power to over three plus one. So that's equal to, um, 5/3. And then that's over. 5/3 with you 3/5. What two acts and then plus are constant. So this is equal to our cost function, See of X. Okay. And we know that. See, Velveeta, eight z certificates so we can plug in this information to solve for a constant K. That is for the eight is equal to 3/5 exes eats. Okay, so what does that give us? Well, two times eight. That some 16. And then we have eight to the power of 5/3 times three cigarettes plus 96/5. That's K and then is able to 58. Okay, so 96/5. 16 times five It's 80/5, so that's equal. Teoh 96 plus 80 which is equal to 176 over five, is equal to 58th and in plus Kitty. I know. Let's jack the hundreds. Every six of five a. Both sides this offer Kate. So 58 times five that's equal to to 95. And that's minus 1 76 Over five 2 to 90 minus 1 36 is equal to 1 14/5 Okay, so we get that are constants K music with 214 over five. Now that we have our constant weaken, this plug that into our cost function to solve for equation so that sea of X is equal to We have 3/5 x to the power of 5/3 plus two x and then plus K, which is 1 14/5

Okay, so we're given, see Prime of X on were also given are fixed costs is equal to eight. What? That means that our cost function value it at zero is equal to eight. Okay. And now we're asked to find, um are cost function given or marginal costs so we can just take the integral of our marginal costs to get our cost function. So that's equal to four X minus five the X. So let's start by using our difference. Rule splitting that up into two inter girls, we get the fallen. Okay, I know. Notice that we have a five and a four, so we use our constant multiple rule to bring or constants outs outside of our integral. So we get the full on. Okay. And now, by using our power rule, we get the full new four x squared over two minus five x of C. So for over two, that's equal to two. Okay, So that's equal to our cost function. No. And now we need to solve for C, which is a constant Well, it's actually live without SK, so we don't get confused to know that see, valued at zero is equal to eight, that is, we'll plug in what we have. Eight is equal to two and r x zero. So we get that okay, is even to eat. Okay, Now, let's put that back into our cost function. To find our equation, we get See, evaluated at X is equal to two X squared, minus five X and in plus Okay, which is eight.


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