Question

Find the derivatives of the following functions.
$(2x^3-5)\tan x$

Answer 1

Let $f\left(x\right)=(2x^3-5)\tan x$

$=2x^3\tan x-5\tan x$

$f^{\prime }\left(x\right)=2[\underset{ProductRule}{\underset{}{3x^2\tan x+x^{3}se{c}^{2}x}]}-5{\sec }^{2}x$

$[\because \frac{d}{dx}(\tan x)={\sec }^{2}x]$

$f^{\prime }\left(x\right)=6x^2\tan x+2x^3{\sec }^{2}x-5{\sec }^{2}x$

$=6x^2\tan x+(2x^3-5){\sec }^{2}x$.