Rules of Differentiation for Trigonometric Functions

In this tutorial we will discuss the basic formulas of differentiation for trigonometric functions.

1. \frac{d}{{dx}}\sin x = \cos x

2. \frac{d}{{dx}}\cos x = - \sin x

3. \frac{d}{{dx}}\tan x = {\sec ^2}x

4. \frac{d}{{dx}}\cot x = - {\csc ^2}x

5. \frac{d}{{dx}}{\sec ^2}x = \sec x\tan x

6. \frac{d}{{dx}}{\csc ^2}x = - \csc x\cot x

 

To remember these formulas, one point to be noted is that these functions come with negative signs starting with the letter C.

 

These are the general formulas for functions with angles:

1. \frac{d}{{dx}}\sin f\left( x \right) = \cos f\left( x \right)\frac{d}{{dx}}f\left( x \right)

2. \frac{d}{{dx}}\cos f\left( x \right) = - \sin f\left( x \right)\frac{d}{{dx}}f\left( x \right)

3. \frac{d}{{dx}}\tan f\left( x \right) = {\sec ^2}f\left( x \right)\frac{d}{{dx}}f\left( x \right)

4. \frac{d}{{dx}}\cot f\left( x \right) = - {\csc ^2}f\left( x \right)\frac{d}{{dx}}f\left( x \right)

5. \frac{d}{{dx}}{\sec ^2}f\left( x \right) = \sec f\left( x \right)\tan f\left( x \right)\frac{d}{{dx}}f\left( x \right)

6. \frac{d}{{dx}}{\csc ^2}f\left( x \right) = - \csc f\left( x \right)\cot f\left( x \right)\frac{d}{{dx}}f\left( x \right)