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2.5 The Chain Rule

# 2.5 The Chain Rule - ♦ If y =[u(x]n where u is a...

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The Chain Rule Section 2.5

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Thm. 2.10 The Chain Rule If y = f(u) is a differentiable function of x , then y = f(g(x)) is a differentiable function of x and ( ( )) '( ( ) '( ( )) d f g x f g x g f x dx = dx du du dy dx dy =
Finding dy/dx Parametrically If all three derivatives exist and , 0 dx dt / / dy dy dt dx dx dt =

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The Power Rule Combined with the Chain Rule

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Unformatted text preview: ♦ If y =[u(x)]n, where u is a differentiable function of x and n is a rational #, then or [ ] dx du x u n dx dy n 1 ) (-[ ] ' 1 u nu u dx d n n-= Joke Time ♦ What do you call a hippo in a phone booth? ♦ Stuck! ♦ What did Leonardo da Vinci’s cow paint? ♦ The Moona Lisa!...
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