Thread: Derivative of a composite function

Hi, I have a test tomorrow and have been trying to do this review question, but I keep getting the wrong answer:

If y = 5u^2 + 3u -1 and u = 18/(x^2 + 5), find dy/dx when x =2.

I found y', then found u'. I subbed x = 2 into u' to get -72/81. Then I subbed 2 into the original u equation, and found u = 2. I subbed that into y' to get 23. 23 X (8/9) for the final answer, but this is wrong. I'm not sure if I made a mistake with derivatives or what, but I'd reallyyy appreciate any help. Thank you!

Show your solution.

This way is easy to check where the mistake is.

y' = 10u + 3

u' = -(2x)(18) / (x^2+5)^2

= -36x/(x^2 + 5)^2


u' (2) = -36(2)/(4+5)^2
= -72/81 --> -8/9

Then u = 18/(2^2) + 5 = 2

So y'(2) = 10(2) + 3 = 23


23 x -8/9 = -184/9

Originally Posted by starswept

y' = 10u + 3

u' = -(2x)(18) / (x^2+5)^2

= -36x/(x^2 + 5)^2


u' (2) = -36(2)/(4+5)^2
= -72/81 --> -8/9

Then u = 18/(2^2) + 5 = 2

So y'(2) = 10(2) + 3 = 23


23 x -8/9 = -184/9

your mistake is at the first step. you have to differentiate implicitly (with respect to x)

y = 5u^2 + 3u - 1

=> y' = 10u*u' + 3u'