Question

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

Answer 1

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

Answer 2

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

Answer 3

no, doubled by g^4

Answer 4

did you try it with an actual example?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

solve C for g' and check

Answer 11

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