Derivative Rules

Common Functions	Function	Derivative
Constant	$c$	$0$
Line	$ax$	$a$
Square	$x^2$	$2x$
Square Root	$\sqrt x$	$\frac{1}{2}x^{-\frac{1}{2}}$
Exponential	$e^x$	$e^x$
	$a^x$	$\ln(a)\times a^x$
Logarithms	$\ln(x)$	$\frac{1}{x}$
	$\log_a(x)$	$\frac{1}{x\times\ln(a)}$
Trigonometry (x is in radians)	$\sin(x)$	$\cos(x)$
	$\cos(x)$	$−\sin(x)$
	$\tan(x)$	$\sec(x)^2$
	$\sec(x)$	$\sec(x)\times \tan(x)$

Rules	Function	Derivative
Multiplication by constant	$cf$	$cf'$
Power Rule	$x^n$	$nx^{n-1}$
Sum Rule	$f + g$	$f' + g'$
Difference Rule	$f - g$	$f' − g'$
Product Rule	$fg$	$f g' + f' g$
Quotient Rule	$\frac{f}{g}$	$\frac{f'g-g'f}{g^2}$
Reciprocal Rule	$\frac{1}{f}$	$-\frac{f'}{f^2}$
Chain Rule	$f \circ g$	$(f'\circ g)\times g'$
Chain Rule (using ’ )	$f(g(x))$	$f'(g(x))g'(x)$

Todo: derivative for trig and anti trig

Antiderivative

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Last update: April 20, 2022
Created: September 17, 2021