Common Derivatives

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Common Derivatives

Function	Derivative w.r.t. [math]x[/math]	Example
[math]\text{Constant}\,[/math]	[math]0\,[/math]	[math]y=4,\qquad \frac{dy}{dx}=0\,[/math]
[math]x^n\,[/math]	[math]nx^{n-1}\,[/math]	[math]y=x^7,\qquad \frac{dy}{dx}=7x^6\,[/math]
[math]e^x\,[/math]	[math]e^x\,[/math]	[math]y=e^x,\qquad \frac{dy}{dx}=e^x\,[/math]
[math]\sin {(ax+b)}\,[/math]	[math]a\cdot \cos {(ax+b)}\,[/math]	[math]y=\sin{(3x+4)},\qquad \frac{dy}{dx}=3\cdot \cos{(3x+4)}\,[/math]
[math]cos(ax+b)\,[/math]	[math]-a\cdot sin(ax+b)\,[/math]	[math]y=cos(3x+4), dy/dx=-3\cdot sin(3x+4)[/math]
[math]tan(ax+b)\,[/math]	[math]a\cdot sec^2(ax+b)\,[/math]	[math]y=tan(3x+4), \frac{dy}{dx}=3\cdot sec^2(3x+4)[/math]
[math]sec(ax+b)[/math]	[math]a\cdot sec(ax+b)\cdot tan(ax+b)[/math]	[math]y=sec(5x-4), dy/dx=5\cdot sec(5x-4)\cdot tan(5x-4)[/math]
[math]cosec(ax+b) [/math]	[math]-a\cdot cosec(ax+b)\cdot cot(ax+b)[/math]	[math]y=cosec(5x-4), dy/dx=-5\cdot cosec(5x-4)\cdot cot(5x-4)[/math]
[math]cot(ax+b)[/math]	[math]-a\cdot cosec^2(ax+b)[/math]	[math]y=cot(3x+4), dy/dx=-3\cdot cosec^2(3x+4)[/math]
[math]log(ax+b)[/math]	[math] a/(ax+b)\,[/math]	[math]y=log(3x+4), dy/dx=3/(3x+4)\,[/math]
[math]a/g(x)[/math]	[math]-ag'(x)/(g(x))^2[/math]	[math]y=1/(x^2+1), dy/dx=-2x/(x^2+1)^2\,[/math]