Question

Differentiate the following w.r.t.x:
$5^x\cdot {\sec }^{-1}2x$

Answer 1

$y=5^x{\sec }^{-1}2x$
$\frac{dy}{dx}=5x\frac{d}{dx}\sec 6-12x+{\sec }^{-1}2x\frac{d}{dx}\left(5^x\right)$
$=5^x\cdot \frac{1}{|2x|\sqrt{4x^2-1}}\left(2\right)+se{c}^{-1}2x\cdot 5^{x}ln5$
$=5^x(\frac{1}{|x|\sqrt{4x^2-1}}+{\sec }^{-1}2xln5)$