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