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)))` |