Differentiation Rules

Derivatives

$\frac{d}{dx}\mathrm{Const.}=0$

$\frac{d}{dx}x=1$

$\frac{d}{dx}{x}^{n}=n{x}^{n-1}$

Derivative of trigonometric functions

$\frac{d}{dx}\mathrm{sin}\left(x\right)=\mathrm{cos}\left(x\right)$

$\frac{d}{dx}\mathrm{cos}\left(x\right)=-\mathrm{sin}\left(x\right)$

$\frac{d}{dx}\mathrm{sin}\left(kx\right)=k\mathrm{cos}\left(kx\right)$

$\frac{d}{dx}\mathrm{cos}\left(kx\right)=-k\mathrm{sin}\left(kx\right)$

$\frac{d}{dx}\mathrm{tan}\left(x\right)=\frac{d}{dx}\frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)}=\frac{1}{{\mathrm{cos}}^{2}\left(x\right)}$

Derivation exponential and logarithmic functions

$\frac{d}{dx}{e}^{x}={e}^{x}$

$\frac{d}{dx}\mathrm{ln}\left(x\right)=\frac{1}{x}$

$\frac{d}{dx}{\mathrm{log}}_{a}\left(x\right)=\frac{1}{x}{\mathrm{log}}_{a}\left(e\right)$

Derivation Calculator

f(x) =
 cl ok Pos1 Ende 7 8 9 / x 4 5 6 * ( ) 1 2 3 - a b c 0 . + sin cos tan ex ln ^ asin acos atan x2 √x xa sinh cosh a⋅sin(b⋅x+c) a⋅e(-b⋅x2+c) a⋅x2+b⋅x+c e(x)⋅sin(x)⋅cos(x)

Differential Calculus

Differentiation Rules

The following are the most important differentiation rules described and illustrated by examples.

• Factor Rule
• Sum rule
• Product Rule
• Quotient Rule
• Chain Rule