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