Answer to Question #344549 in Calculus for kristine

Question

Differentiate the trigonometric functions

1. = 2 sec x + tan x

2. y = sin x/ 1 + COS X

3. y = cos x cot x

Answer 1

1.

$$y'=(\sec x+\tan x)'=-\dfrac{1}{\cos^2 x}(-\sin x)+\dfrac{1}{\cos ^2 x}$$

$$=\dfrac{\sin x+1}{\cos ^2 x}=(\sin x+1)\sec ^2 x$$

2.

$$y'=(\dfrac{\sin x}{1+\cos x})'=\dfrac{\cos x(1+\cos x)+\sin ^2x}{(1+\cos x)^2}$$

$$=\dfrac{1+\cos x}{(1+\cos x)^2}=\dfrac{1}{1+\cos x}$$

3.

$$y'=(\cos x\cot x)'=-\sin x\cot x-\dfrac{\cos x}{\sin^2 x}$$

$$=-\cos x-\cot x\csc x$$