Brittany W.

asked • 07/12/15

Suppose f(0)=5, f'(0)=2, f(1)=3, f'(1)=6, g(1)=5, g'(1)=-8, and H(x)=f(ln(x))+ln(g(x)). Find dH/dx||||x=1. H'(1)= ?

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Muhammad C. answered • 07/13/15

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H'(x) = f'(ln (x)) + g'(x)/g(x)
 
H'(1) = f'(ln 1) + g'(1)/g(1)
 
H'(1) = f'(0) + g'(1)/g(1)
 
H'(1) = 2 + -8/5 = 2/5
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Michael W.

Muhammad, for the derivative of f(ln(x)), doesn't the Chain Rule apply to that, too?  Wouldn't the derivative of that part be f'(ln(x)) * 1/x, where 1/x is the derivative of ln(x)?
 
Ultimately, it doesn't matter, because we're plugging in x = 1...so 1/x ends up being 1.  Moot point.  :)  But just wanted to make sure the answer was technically accurate and if I was missing something.
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07/13/15

Muhammad C.

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The Chain Rule does apply, but I didn't add it being that we would be multiplying the other part by 1. 
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07/13/15

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