Derivative calculator

How to use the derivative calculator

Type the function with x as the variable and press "Differentiate". You can use the usual textbook notation: sin, cos, tan, ln (natural log), log (base 10), sqrt, arcsin and arctan. Multiply with * or by writing the factors next to each other (3x^2), and put exponents with more than one term in brackets, as in e^(2x).

The answer comes out simplified. For the first derivative it is also checked against a numerical approximation at several points. If something doesn't add up, you get a warning instead of a doubtful answer.

Three examples worked out with this calculator

• Product rule: $\left(x^2\sin x\right)' = 2x\sin x + x^2\cos x$
• Chain rule: $\left(\ln(x^2+1)\right)' = \frac{2x}{x^2+1}$
• Quotient rule: $\left(\frac{x^2+1}{x-3}\right)' = \frac{x^2-6x-1}{(x-3)^2}$

For the tangent line to f at x = a you need f(a) and f'(a): type the function, enter the point in "Value at x =" and you have the slope. Going the other way? The integral calculator finds antiderivatives and definite integrals.