Derivative Calculator
Differentiate functions, simplify derivatives, evaluate slopes, and build tangent-line equations
Enter one single-variable expression. Use ^ for powers, log(x) or ln(x) for natural log, and pi for pi.
Differentiate with respect to this symbol.
Optional point for slope and tangent line.
Digits used when showing numeric slopes.
Try an example
Derivative Result
Differentiate with respect to x
Simplified derivative
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Second derivative
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Slope
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Function Value
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Point
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Tangent line
Enter an evaluation point to calculate a tangent line.
Calculation Steps
- Enter a function to see symbolic steps.
How This Derivative Calculator Works
The calculator parses your expression, differentiates it symbolically, simplifies the result, and optionally evaluates the slope at a point.
Symbolic rules
Differentiation is handled by mathjs for common algebraic, trig, exponential, logarithmic, quotient, and chain-rule expressions.
Slope at a point
If you enter an evaluation point, the simplified derivative is evaluated there to estimate the instantaneous rate of change.
Tangent line
The tangent line uses the point-slope form y - f(a) = f'(a)(x - a) for the selected variable and point.
Derivative Examples
Use these formats as starting points for common calculus problems.
Power rule
Enter 5x^4 - 3x^2 + 9 to differentiate a polynomial term
by term.
Chain rule
Enter sin(x^2) or e^(2x) for nested
functions.
Logarithms
Enter ln(x) or log(x) for natural log, and
log10(x) for base 10.
Tangent slope
Add an evaluation point to calculate f(a), f'(a), and the point-slope tangent equation.
Derivative Calculator FAQ
Common questions about notation, supported functions, and point evaluation.
What kinds of derivatives can this calculator solve?
It handles common single-variable expressions with powers, products, quotients, roots, trigonometric functions, exponential functions, and logarithms.
Can I evaluate the derivative at a point?
Yes. Enter a value such as 2, -1.5, pi, or pi/2 in the evaluation field to calculate the slope, the function value, and a tangent-line equation.
Does log mean natural logarithm here?
Yes. In calculus notation, log is treated as the natural logarithm. You can also enter ln(x), which is normalized to log(x), or use log10(x) for base-10 logarithms.
Can this calculator solve multivariable derivatives?
It differentiates one selected variable at a time. Keep all other symbols out of the expression so the result stays clear and deterministic.
Why can a derivative be undefined at a point?
Some functions have domain restrictions, vertical tangents, cusps, or discontinuities. The symbolic derivative can exist as an expression even when a specific point is not valid.