derivative rules

d/dx [sin(x)]

\cos\left(x\right)

d/dx [cos(x)]

-\sin\left(x\right)

d/dx [tan(x)]

\sec^2\left(x\right)

d/dx [csc(x)]

-\csc\left(x\right)\cot\left(x\right)

d/dx [sec(x)]

\sec\left(x\right)\tan\left(x\right)

d/dx [cot(x)]

-\csc^2\left(x\right)

d/dx(sin^-1(u))

\frac{u^{\prime}}{\sqrt{1-u^2}}

d/dx(cos^-1(u))

-\frac{u^{\prime}}{\sqrt{1-u^2}}

d/dx(tan^-1(u))

\frac{u^{\prime}}{1+u^2}

d/dx(cot^-1(u))

-\frac{u^{\prime}}{1+u^2}

d/dx(sec^-1(u))

\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}  

d/dx(csc^-1(u))

-\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}