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