How do you find the derivative of #f(x)=ln(2x^2+1)^5#?

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Answer 1 · 2016-12-13T04:31:58

There are three "layers" in this function.

#(f(g(h(x)))#

Going from:
outside
#darr#
inside

#f(x)=x^5#
#f'(x)=5(x)^4#

#g(x)=ln(x)#
#g'(x)=1/(x)#

#h(x)=(2x^2+1)#
#h'(x)=4x#

To find the derivative, we need to apply this rule.

Thus:

#f'(x)=[5ln(2x^2+1)^4]/(2x^2+1)*4x=(20xln(2x^2+1))/(2x^2+1)#