Differentiation of trigonometry rules

Here are the differentiation rules for the basic trigonometric functions:

• The derivative of $\sin(x)$ is $\cos(x)$. $$\frac{d}{dx}(\sin(x)) = \cos(x)$$
• The derivative of $\cos(x)$ is $-\sin(x)$. $$\frac{d}{dx}(\cos(x)) = -\sin(x)$$
• The derivative of $\tan(x)$ is $\sec^2(x)$. $$\frac{d}{dx}(\tan(x)) = \sec^2(x)$$
• The derivative of $\cot(x)$ is $-\csc^2(x)$. $$\frac{d}{dx}(\cot(x)) = -\csc^2(x)$$
• The derivative of $\sec(x)$ is $\sec(x)\tan(x)$. $$\frac{d}{dx}(\sec(x)) = \sec(x)\tan(x)$$
• The derivative of $\csc(x)$ is $-\csc(x)\cot(x)$. $$\frac{d}{dx}(\csc(x)) = -\csc(x)\cot(x)$$