Table of the Derivatives

Related calculator: Online Derivative Calculator with Steps

Below is the list of the most common derivatives.

`f(x)`	`f'(x)`
Power Rule
`x^n`	`nx^(n-1)`
Exponential Function
`a^x`	`ln(a)a^x`
`e^x`	`e^x`
Logarithmic Function
`log_a(x)`	`1/(xln(a))`
`ln\|x\|`	`1/x`
Trigonometric Functions
`sin(x)`	`cos(x)`
`cos(x)`	`-sin(x)`
`tan(x)`	`1/(cos^2(x))=sec^2(x)`
`cot(x)`	`-1/(sin^2(x))=-csc^2(x)`
`sec(x)=1/(cos(x))`	`sec(x)tan(x)`
`csc(x)=1/(sin(x))`	-`csc(x)cot(x)`
Inverse Trigonometric Functions
`arcsin(x)`	`1/(sqrt(1-x^2))`
`arccos(x)`	`-1/(sqrt(1-x^2))`
`arctan(x)`	`1/(1+x^2)`
`text(arccot)(x)`	`-1/(1+x^2)`
`text(arcsec)(x)`	`1/(xsqrt(x^2-1))`
`text(arccsc)(x)`	`-1/(xsqrt(x^2-1))`
Hyperbolic Functions
`sinh(x)`	`cosh(x)`
`cosh(x)`	`sinh(x)`
`tanh(x)`	`1/(cosh^2(x))=text(sech)^2(x)`
`coth(x)`	`-1/(sinh^2(x))=-text(csch)^2(x)`
`text(sech)(x)=1/(cosh(x))`	`-text(sech)(x)tanh(x)`
`text(csch)(x)=1/(sinh(x))`	`-text(csch)(x)coth(x)`
Inverse Hyperbolic Functions
`text(arcsinh)(x)`	`1/(sqrt(x^2+1))`
`text(arccosh)(x)`	`1/(sqrt(x^2-1))`
`text(arctanh)(x)`	`1/(1-x^2)`
`text(arccot)text(h)(x)`	`1/(1-x^2)`
`text(arcsec)text(h)(x)`	`-1/(xsqrt(1-x^2))`
`text(arccsc)text(h)(x)`	`-1/(\|x\|sqrt(1+x^2))`
Differentiation Rules
`c`	`0`
`g(x)+h(x)`	`g'(x)+h'(x)`
`g(x)-h(x)`	`g'(x)-h'(x)`
`c*g(x)`	`c*g'(x)`
`g(x)h(x)`	`g'(x)h(x)+g(x)h'(x)`
`(g(x))/(h(x))`	`(g'(x)h(x)-g(x)h'(x))/(h^2(x))`
`g(h(x))`	`g'(h(x))*h'(x)`
`f^(-1)(x)`	`1/(f'(f^(-1)(x)))`