All Maths Formulas

Algebra

(c \cdot f (x))' = c \cdot f' (x)

$\left(c \cdot f(x)\right)' = c \cdot f'(x)$

(f \pm g)' = f' \pm g'

$\left(f \pm g \right)' = f' \pm g'$

Product rule

(f \cdot g)' = f' \cdot g + f \cdot g'

$(f \cdot g)' = f' \cdot g + f \cdot g'$

Quotient rule

(f g)' = f ' \cdot g - f \cdot g ' g 2

$\left( \frac{f}{g} \right)' = \frac{ f'\cdot g - f \cdot g' }{g^2}$

Chain rule

(f (g (x)))' = f' (g (x)) \cdot g' (x)

$\left( f \left(g(x) \right) \right)' = f'(g(x)) \cdot g'(x)$

d d x (C) = 0

$\frac{d}{dx} (C) = 0$

d d x (x) = 0

$\frac{d}{dx} (x) = 0$

d d x (x n) = n \cdot x n - 1

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

d d x (sin x) = cos x

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

d d x (cos x) = - sin x

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

d d x (tan x) = 1 cos 2 x

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

d d x (sec x) = sec x \cdot tan x

$\frac{d}{dx} ( \sec x) = \sec x \cdot \tan x$

d d x (csc x) = - csc x \cdot cot x

$\frac{d}{dx} (\csc x) = - \csc x \cdot \cot x$

d d x (cot x) = - 1 sin 2 x

$\frac{d}{dx} (\cot x) = -\frac{1}{ \sin^2x }$

d d x (arcsin x) = 1 1 - x 2 - - - - - \sqrt

$\frac{d}{dx} (\arcsin x) = \frac{1}{ \sqrt{1-x^2} }$

d d x (arccos x) = - 1 1 - x 2 - - - - - \sqrt

$\frac{d}{dx} (\arccos x) = -\frac{1}{\sqrt{1-x^2}}$

d d x (arctan x) = 1 1 + x 2

$\frac{d}{dx} (\arctan x) = \frac{1}{1+x^2}$

d d x (a x) = a x \cdot ln a

$\frac{d}{dx} (a^x) = a^x \cdot \ln a$

d d x (e x) = e x

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

d d x (ln x) = 1 x, x > 0

$\frac{d}{dx} (\ln x) = \frac{1}{x} , x > 0$

d d x (ln | x |) = 1 x, x \neq 0

$\frac{d}{dx} (\ln |x|) = \frac{1}{x} , x \ne 0$

d d x (log a x) = 1 x \cdot ln a, x > 0

$\frac{d}{dx} \left( \log_a x \right) = \frac{1}{x\cdot \ln a} , x > 0$