Difference between revisions of "Derivative/Formulas"
Mathforce1 (talk | contribs) (→List of formulas) |
m (Reverted edits by Mathforce1 (Talk) to last version by 1=2) |
||
| Line 1: | Line 1: | ||
| − | + | == List of formulas == | |
| + | |||
| + | {| style="margin: 1em auto 1em auto; height:1000px" | ||
| + | | <math>\frac d{dx}(cf(x)) = c\left(\frac d{dx} f(x)\right)</math> where c is a constant | ||
| + | |- | ||
| + | | <math>(f(x) + g(x))' = f'(x) + g'(x)</math> | ||
| + | |- | ||
| + | | <math>(f(x)-g(x))'=f'(x)-g'(x)</math> | ||
| + | |- | ||
| + | | <math>\left(u(x)\times v(x)\right)'=u(x)v'(x)+u'(x)v(x)</math> | ||
| + | |- | ||
| + | | <math>\left(\frac{u(x)}{v(x)}\right)' = \frac{u'(x)v(x) - u(x)v'(x)}{(v(x))^2}</math> | ||
| + | |- | ||
| + | | <math>(f(g(x)))' = f'(g(x))g'(x)</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} x^n = n x^{n-1}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} (f(x))^n =n f(x)^{n-1} f'(x)</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \sin x = \cos x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \cos x = -\sin x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \tan x = \sec^2 x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \sec x = \sec x \tan x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \csc x = -\csc x\cot x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \cot x = -\csc^2 x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} e^x = e^x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} a^x = (\ln a) a^x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \ln x = \frac 1x</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \log_b x =\frac{\log_b e}{x} </math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \arcsin x = \frac 1{\sqrt{1-x^2}}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \arccos x = -\frac 1{\sqrt{1-x^2}}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \arctan x = \frac 1{1+x^2}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \mathrm{arcsec \ } x = \frac 1{\mid x \mid\sqrt{x^2-1}}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \mathrm{arccsc \ } x = - \frac 1{x\sqrt{x^2 - 1}}</math> | ||
| + | |- | ||
| + | | <math>\frac d{dx} \mathrm{arccot \ } x = - \frac 1{1+x^2}</math> | ||
| + | |} | ||
== See also == | == See also == | ||
* [[Calculus]] | * [[Calculus]] | ||
* [[Derivative]] | * [[Derivative]] | ||
where c is a constant
