Question

Let f(x)=−2sec^2(x^2). Find f′(x).

Answer 1

Given:

$f(x)=2\sec ^2(x^2)$

Differentiate with respect to x

$\begin{gathered} f^{\prime}(x)=2\lbrack2\sec (x^2)\rbrack\lbrack\sec (x^2)\tan (x^2)\rbrack\lbrack2x\rbrack \\ f^{\prime}(x)=8x\sec ^2(x^2)\tan (x^2) \end{gathered}$