Derivative Calculator

This calculator evaluates derivatives using analytical differentiation. It will also find local minimum and maximum, of the given function. The calculator will try to simplify result as much as possible.

There are examples of valid and invalid expressions at the bottom of the page.

Result

$$ \begin{aligned} f(x) &= \sin(x) \\ \\\end{aligned} $$
$$ \begin{aligned} f~'(x) &= \cos(x) \\ \\\end{aligned} $$
$$ \begin{aligned} f~''(x) &= −sin(x) \\ \\\end{aligned} $$
$$ \begin{aligned} f~'''(x) &= −cos(x) \\ \\\end{aligned} $$

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Help

1. For powers use ^. Example: x12= x^12 ; ex+2= e^(x+2)
2. For square root use "sqrt". Example: x+1−−−−−√= sqrt(x+1).
3. Supported constants: e, pi
4. Supported functions: sqrt, ln ( use 'ln' instead of 'log'), e (use 'e' instead of 'exp')
Trigonometric functions: sin cos tan cot sec csc
Inverse trigonometric functions: acos asin atan acot asec acsc
Hyperbolic functions: sinh, cosh, tanh, coth, sech, csch

Examples of valid and invalid expressions


Function to integrate Correct syntax is Incorrect syntax is
$$ (2x+1)^6 $$ (2x+1)^6 [2x+1]^6
$$ \frac{10x + 1}{x^2-4} $$ (10x+1)/(x^2-4) 10x+1/x^2-4
$$ \left(ln(x)\right)^2 $$ ln(x)^2 ln^2(x)
$$ x ~ ln\left(\frac{x-1}{x+1}\right) $$ x*ln((x-1)/(x+1)) x*ln(x-1)/(x+1)



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