derivatives of trigonometric functions

$$\begin{array}{rl}& \text{The derivative of the sine function is the cosine function:}\\ & \frac{d}{dx}(\sin x)=\cos x.\end{array}$$ $$\begin{array}{rl}& \text{And the derivative of the cosine function is the negtive of the sine function:}\\ & \frac{d}{dx}(\cos x)=-sinx.\end{array}$$ $$\begin{array}{rl}& \text{The derivatives of the other trigonometric functions:}\\ & \frac{d}{dx}(\tan x)={\sec }^{2}x\frac{d}{dx}(\cot x)=-{\csc }^{2}x\\ & \frac{d}{dx}(\sec x)=\sec x\tan x\frac{d}{dx}(\csc x)=-\csc x\cot x\end{array}$$