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)))`