If #f(x)= tan5 x # and #g(x) = 2x^2 -1 #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2016-01-02T16:18:59

#20xsec^2(10x^2-5)#

The chain rule states that

#d/dx[f(g(x))]=f'(g(x))*g'(x)#

First, find #f'(g(x))#.

#f'(x)=5sec^2(5x)#

Note that this required the chain rule as well.

#f'(g(x))=5sec^2(5(2x^2-1))=5sec^2(10x^2-5)#

Now, find #g'(x)#.

#g'(x)=4x#

Combine.

#d/dx[f(g(x))]=5sec^2(10x^2-5)*4x=20xsec^2(10x^2-5)#