Table of the Derivatives
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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)))` |