# Derivative Rules for Basic Functions

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

## Table of Derivatives

Function Derivative
$$y=c$$ $${y}'=0$$
$$y=x$$ $${y}'=1$$
$$y=\frac{1}{x}$$ $${y}'=-\frac{1}{x^{2}}$$
$$y=\sqrt{x}$$ $${y}'=\frac{1}{2\sqrt{x}}$$
$$y=x^{n}$$ $${y}'=nx^{n-1}$$
$$y=\sin x$$ $${y}'=\cos x$$
$$y=\cos x$$ $${y}'=-\sin x$$
$$y=\tan x$$ $${y}'=\frac{1}{\cos^{2} x}$$
$$y=\cot x$$ $${y}'=-\frac{1}{\sin^{2} x}$$
$$y=a^{x}$$ $${y}'=a^{x}\ln a$$
$$y=e^{x}$$ $${y}'=e^{x}$$
$$y=\log_{a}x$$ $${y}'=\frac{1}{x \ln a}$$
$$y=\ln x$$ $${y}'=\frac{1}{x}$$
$$y=\arcsin x$$ $${y}'=\frac{1}{\sqrt{1-x^{2}}}$$
$$y=\arccos x$$ $${y}'=-\frac{1}{\sqrt{1-x^{2}}}$$
$$y=\arctan x$$ $${y}'=\frac{1}{1+x^{2}}$$
$$y=\mathrm{arccot}\, x$$ $${y}'=-\frac{1}{1+x^{2}}$$