Derivative Calculator - Differentiate Any Function Step by Step Online
Derivative Calculator
First, second and third derivatives, evaluated at a point
Symbolic Results
You get an exact formula, not just a number, rendered as proper notation and as plain text you can copy.
Higher Orders
Go up to the third derivative to study concavity, inflection points or jerk in physics.
Tangent Line
Give a point and see the slope there and the equation of the tangent line.
Runs Locally
The differentiation happens in your browser; your input is never uploaded.
The Rules Behind the Answer
A derivative measures how fast a function changes. The calculator applies the same rules you learn in class: the power rule (xn becomes n·xn-1), the product and quotient rules, the chain rule for functions inside functions, and the standard derivatives of sin, cos, tan, ex and ln x. The result is then simplified, so it may look different from a hand-written answer while being equal to it.
In the output, log(x) means the natural logarithm ln x, and sec is 1/cos. Letters other than the chosen variable, such as a or k, are treated as constants, which is handy for formulas like a·x2 + b·x. Functions with corners or jumps, such as abs or floor, are not differentiable everywhere; abs is handled where it is smooth, while floor and round are rejected.
Key Takeaways
- Exact formulas: Results are symbolic and simplified, with a plain-text copy for your notes.
- Natural input: Implied multiplication, ln, sqrt and the √ and π symbols are understood.
- Check your work: Evaluate at a point to compare with a value you computed by hand.