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.

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

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