Answer to Question #150326 in Calculus for stefanus weyulu

Question

Differentiate the following function
g(x) = e
−5x +

1
x
− tan x
3 p
x
2 + 1 
.

Answer 1

$$g'(x)=\bigg(e^{-5x}+(\dfrac{1}{x}-\tan x)^3\sqrt{x^2+1}\bigg)'$$

$$=-5e^{-5x}+3(\dfrac{1}{x}-\tan x)^2(-\dfrac{1}{x^2}-\dfrac{1}{\cos^2x})\sqrt{x^2+1}$$

$$+(\dfrac{1}{x}-\tan x)^3\dfrac{x}{\sqrt{x^2+1}}$$