Math Wiki

Derivative formulas

1,078pages on
this wiki
Add New Page
Talk0 Share

The derivative of any polynomial function of one variable is easily obtained. If c\in\R (or a constant function) and f,g:D\to\R are both differentiable on some set D' , then so are c\cdot f , f+g , -f , and f\cdot g . If, in addition, g is nonzero on D' , then \frac{1}{g} (and also \frac{f}{g}) are differentiable on D' . Also, if f is differentiable on g\left(D'\right), then f\circ g is differentiable on D' . For the trivial case of f(x)=a , for some constant a (a degree 0 polynomial):

a'=0 [Proof]

For any r\in\R :

(x^r)'=rx^{r-1} [Proof]

Which covers any single variable polynomial function. Derivatives of non-polynomial functions require additional rules.

For any real-valued differentiable functions f(x),g(x) :

  • (-f(x))'=-f'(x)
  • \left(\frac{1}{g(x)}\right)'=-\frac{g'(x)}{g(x)^2}

Trigonometric functions:

  • \frac{d}{dx}(\cos(x))=-\sin(x)
  • \frac{d}{dx}(\tan(x))=\sec^2(x)
  • \frac{d}{dx}(\csc(x))=-\csc(x)\cot(x)
  • \frac{d}{dx}(\sec(x))=\sec(x)\tan(x)
  • \frac{d}{dx}(\cot(x))=-\csc^2(x)
  • \frac{d}{dx}(\arcsin(x))=\frac{1}{\sqrt{1-x^2}}
  • \frac{d}{dx}(\arccos(x))=-\frac{1}{\sqrt{1-x^2}}
  • \frac{d}{dx}(\arctan(x))=\frac{1}{1+x^2}
  • \frac{d}{dx}(\arcsec(x))=\frac{1}{|x|\sqrt{x^2-1}}
  • \frac{d}{dx}(\arccsc(x))=-\frac{1}{|x|\sqrt{x^2-1}}
  • \frac{d}{dx}(\arccot(x))=-\frac{1}{1+x^2}

Logarithmic and exponential functions:

  • \frac{d}{dx}(e^x)=e^x
  • \frac{d}{dx}(a^x)=a^x\ln(a)
  • \frac{d}{dx}(\log_a(x))=\frac{1}{\ln(a)x}

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

Also on Fandom

Random Wiki