1. ## Chain rule help

the question is find dy/dx at the indicated value of x

y = sqrt[u^2 +5], where u = (1-x)/(1+x) ; x=-2

the answer the book has is 6/sqrt14 but I am getting 3/sqrt14

here is my work

1/2[u^2 + 5]^(-1/2) * 2u * d/dx(u)

comes down to [1/2] * 14^(-1/2) * (-6) * (-1)

giving me 6/2sqrt14 -> 3/sqrt14

thank you!

2. ## Re: Chain rule help

First I'll try to retype your given equations.

$y =\sqrt{u^2+5} \quad \text{ and } \quad u=\frac{1-x}{1+x} \\ \frac{dy}{dx}=\frac{2u}{2\sqrt{u^2+5}}\frac{du}{dx }=\frac{u}{\sqrt{u^2+5}}\frac{du}{dx} \quad \text{ and } \quad \\ \frac{du}{dx}=\frac{(-1)(1+x)+(-1)(1-x)}{(1+x)^2}=\frac{-2}{(1+x)^2}$

Try to plug in u and du/dx into dy/dx

3. ## Re: Chain rule help

oh, I was forgetting the quotient rule. thank you