Rules of Differentiation for Trigonometric Functions

In this tutorial we discuss 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

For remember these formulas one point to be noted that those function comes with negative sign starting with alphabet C.

Now general formulas when any function is given in terms angles, the following formula of the form

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)