anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
This seems to be using u-substitution try this: https://www.khanacademy.org/math/integral-calculus/integration-techniques/u_substitution/v/u-substitution
DanJS
  • DanJS
From a to b, did you divide by [g(x)]^4 ?
anonymous
  • anonymous
no, doubled by g^4

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misty1212
  • misty1212
did you try it with an actual example?
misty1212
  • misty1212
\[g(x)=\sin(x), f(x)=\frac{1}{\sin^3(x)}\]
anonymous
  • anonymous
way to try with numbers? f(x) and g(x) can be any equations
misty1212
  • misty1212
\[f'(x)=\frac{-3\cos(x)}{\sin^4(x)}\] and so
misty1212
  • misty1212
\[g'(x)=-\frac{1}{3}f'(x)g^4(x)\] or \[\cos(x)=\cos(x)\]
anonymous
  • anonymous
but i want to do implicit derivering, and stay with f(x) and g(x). are (3) and (c) the same?
DanJS
  • DanJS
solve C for g' and check
anonymous
  • anonymous
OK, got it, thanks! in (c): \[fg^3 \] = 1

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