## anonymous one year ago the question is in the picture, why when i go from (1) or (a) i get different equation for the same g' ? https://dl.pushbulletusercontent.com/X0Sg1DgSq9wucZsrYb1KCdHUr2VWY2rJ/IMG_20150701_161911.jpg

1. anonymous

This seems to be using u-substitution try this: https://www.khanacademy.org/math/integral-calculus/integration-techniques/u_substitution/v/u-substitution

2. DanJS

From a to b, did you divide by [g(x)]^4 ?

3. anonymous

no, doubled by g^4

4. misty1212

did you try it with an actual example?

5. misty1212

$g(x)=\sin(x), f(x)=\frac{1}{\sin^3(x)}$

6. anonymous

way to try with numbers? f(x) and g(x) can be any equations

7. misty1212

$f'(x)=\frac{-3\cos(x)}{\sin^4(x)}$ and so

8. misty1212

$g'(x)=-\frac{1}{3}f'(x)g^4(x)$ or $\cos(x)=\cos(x)$

9. anonymous

but i want to do implicit derivering, and stay with f(x) and g(x). are (3) and (c) the same?

10. DanJS

solve C for g' and check

11. anonymous

OK, got it, thanks! in (c): $fg^3$ = 1