Derivative Calculator – Free With Rules Shown
This derivative calculator finds the derivative of a function and tells you which rules it used. Type a function like x^2*sin(x), e^(3x) or ln(x)/x, choose the variable and the order, and you get the simplified derivative. It applies the power, product, quotient and chain rules, and it can also evaluate the derivative at a point. Everything runs on your device with no account and no upload.
Derivative Calculator
Find first and higher derivatives of a function and see the rules used.
How to use the Derivative Calculator
- Type the function, for example x^3 + 2x or sin(x)*e^x.
- Keep x as the variable or change it to another letter.
- Choose the order: 1 for the first derivative, 2 for the second, and so on.
- Optionally enter a value to get the derivative at that point, then read the result.
Differentiation rules
Power: d/dx xโฟ = n·xโฟ⁻¹. Product: (uv)′ = u′v + uv′. Quotient: (u/v)′ = (u′v − uv′)/v². Chain: (f(g))′ = f′(g)·g′.
Features
- First to sixth order derivatives
- Power, product, quotient and chain rules
- Trig, inverse trig, exponential, log and root functions
- Value of the derivative at a point
- Exact fractions in the answer
- Free and private
Frequently asked questions
How do I find the derivative of a function?
Type the function and read the result. The tool applies differentiation rules symbolically, then simplifies the answer, so d/dx of x^2 gives 2*x.
Which rules does the calculator use?
It uses the power, sum, product, quotient and chain rules, plus the standard derivatives of sine, cosine, tangent, exponentials, logarithms, roots and inverse trig functions. The rules used are listed under the answer.
Can I find a second derivative?
Yes. Set the order to 2 for the second derivative, 3 for the third, and so on up to 6.
What does the derivative at a point mean?
It is the slope of the tangent line to the curve at that x value, or the instantaneous rate of change. Enter a number in the point box to see it.
Does the answer always look simplified?
The tool combines like terms and orders factors, but a result can differ in form from a textbook answer while being equal. You can check by graphing or substituting a value.