How do you use the chain rule to differentiate #y=4(x^2+1)^2#?

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Answer 1 · 2016-12-07T07:00:31

#dy/dx =16x(x^2+1)#

#y=4(x^2+1)^2#

The chain rule states that: #d/dx (f(g(x)) = f'(g(x))*g'(x)#

Here: #f(x) = 4(g(x))^2# where #g(x)=x^2+1#

Applying the chain rule:

#dy/dx=4*2(x^2+1) * d/dx(x^2+1)#

#=8(x^2+1)*2x#

#=16x(x^2+1)#