# 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)))