Find the value of (f o g)' at the given value of x.(adsbygoogle = window.adsbygoogle || []).push({});

f(u)=u^5+1, u=g(x)=sqrt x, x = 1

So I found the derivate of f(u) & of u.

f'(u)= 5u^4 & u'= 1/(2sqrt x)

Then I plugged 1 in for x in u' & got 1/2. What I don't understand is why I can't just then plug 1/2 in for u & solve.

Another example

f(u)= 2u/(u^2+1), u=g(x)= 10x^2+x+1, x=0

Here I did the same, found the derivative of f'(u) & u'.

f'(u) = -2u^2+2/(u^2+1)^2 & u'=20x+1

Then I plugged in zero for u' & got 1. If you then plug 1 into f'(u), you get 0. Which matches the answer in the back of the book, but the first one does not using the same technique. Somewhere I think my knowledge of the concept is incomplete. Any help would be welcome.

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# Homework Help: Composite Derivative

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