Derivative Solver
Enter a function, choose the variable and the order, and get the derivative with each rule explained.
Learn the method
Choose the rule before simplifying
Recognizing the structure of a function makes differentiation easier to follow.
Worked example
- 1For f(x)=x²eˣ, identify a product of x² and eˣ.
- 2Differentiate each factor: (x²)′=2x and (eˣ)′=eˣ.
- 3Combine: f′(x)=2xeˣ+x²eˣ=eˣ(x²+2x).
A formula for a derivative is only valid where the original function is defined and differentiable.
What this derivative solver does
- First, second and higher-order derivatives with respect to any variable
- Each step names the rule: power, product, quotient, chain, implicit or logarithmic differentiation
- Graph of the function with the tangent line at any point you choose
- The derivative is recomputed independently and compared at sample points
How to use it
- Type the function. Use * for products, ^ for powers, and functions like sin(), ln(), e^x.
- Choose the variable and the order of the derivative.
- Press Solve to see the derivative, the rules applied and the graph with its tangent line.
Questions about the derivative solver
Does the derivative solver explain which rule was used?
Yes. Each step names the rule (product, quotient, chain, power, etc.) and shows the expression obtained after applying it, followed by the simplified result.
Can it compute higher-order derivatives?
Yes. Set the order to 2, 3 or more. The solver differentiates step by step and simplifies between orders.
Does it support implicit differentiation?
Yes. Enter the equation, for example x^2 + y^2 = 25, and ask for dy/dx; the solver treats y as a function of x.
How is the derivative checked?
The function is differentiated independently by the website's math engine and compared with the stated derivative at many sample points.