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