Enter a function of x and get its derivative symbolically, up to the third order, with a numeric check.
How the derivative calculator works
This calculator differentiates symbolically rather than numerically, applying the product, quotient and chain rules to build an exact expression. It handles polynomials, trigonometric functions, exponentials, logarithms and roots.
It also evaluates the derivative at a point and compares it against a central-difference numeric slope, so you can see the symbolic answer confirmed by an independent method.
Step by step
- Type your function using x, +, -, *, /, ^ and functions like sin, cos, ln, sqrt.
- Choose the order of derivative you want.
- Enter a value of x to evaluate the derivative there.
How the number is calculated
power rule: d/dx xⁿ = n·xⁿ⁻¹
product: (uv)′ = u′v + uv′ · quotient: (u/v)′ = (u′v − uv′)/v²
chain: f(g(x))′ = f′(g(x))·g′(x)
A worked example
The calculator opens with a function f of x^3 – 5x^2 + 2x – 7. On those figures the derivative is 3·x^2-10·x+2. Underneath, f comes out at x^3-5·x^2+2·x-7 and f′ at 3·x^2-10·x+2. Change any field and every figure updates as you type.
Common questions
What notation can I use?
Standard operators plus implicit multiplication — 2x, 3sin(x) and x(x+1) all parse. Functions available include sin, cos, tan, ln, log, exp, sqrt and abs.
Why is a numeric check shown?
As a sanity test. If the symbolic derivative and the numeric slope disagree, something in the input was not what you intended.
Can it do partial derivatives?
No — this handles single-variable functions of x. For partial derivatives, differentiate with respect to one variable at a time by hand.