What kinds of functions can this calculator differentiate?

It differentiates polynomials, rational functions, products and quotients, all six trigonometric functions (sin, cos, tan, sec, csc, cot), inverse trig (arcsin, arccos, arctan), hyperbolic functions, exponentials including eˣ and aˣ, natural and common logarithms, square roots and any composition of these via the chain rule.

Does it show the working step by step?

Yes. Every result includes a numbered breakdown of the rules applied — constant rule, power rule, sum and difference rules, constant-multiple rule, product rule, quotient rule, chain rule, trig rules, exponential and logarithm rules — so students can match each line back to their textbook.

Can it evaluate the derivative at a specific point?

Yes. Open the optional 'Evaluate at x = …' field below the keypad, type a numeric value (or π, e or a simple expression), and the calculator returns the value of f'(x) at that point — the slope of the tangent line.

What is the chain rule?

The chain rule says that to differentiate a composite function f(g(x)), you multiply the derivative of the outer function (evaluated at g) by the derivative of the inner function: d/dx [f(g(x))] = f'(g(x)) · g'(x). The calculator applies it automatically whenever a function takes a non-trivial argument.

Why is my derivative not fully simplified?

The calculator applies the rules of differentiation faithfully and does light algebraic simplification, but does not attempt full algebraic simplification by design — leaving the structure intact makes it easier to see which rule produced which term. You can simplify the expression further by hand if needed.

𝑑/𝑑𝑥 Calculus Derivative Calculator

Differentiate any function step-by-step. Type the expression directly or use the specialised keyboard for trig, log, exponential and power functions.

Enter the function f(x) (use x as the variable)

3x^2 + 2x - 5

Tips: powers need ^ — type x^2 for x² (just x2 means x·2). Multiplication is implicit — 2x, 3sin(x) and 5(x+1) all work. Use sqrt(x) for √x, pi for π and e for Euler's number. The expression is treated as f(x); the result is f'(x).

x² 3x² + 2x − 5 x³ · sin(x) (x²+1)/(x−1) sin(2x+1) e^(x²) ln(x) 1/x √(x²+1) tan(x)

Evaluate the derivative — optional

Slope at x =

Leave blank for the symbolic derivative. Fill in a value to also see f'(x₀) — the slope of the tangent line at that point.

Derivative

About the Calculus Derivative Calculator

The Calculus Derivative Calculator finds the derivative of a function with respect to x and shows the working line by line. It is built for students, educators and self-learners who want to see why an answer is correct, not just the final result. Every step names the rule that was applied — power rule, sum rule, constant-multiple rule, product rule, quotient rule, chain rule, trigonometric rules, exponential rule or logarithm rule — so you can match it back to your textbook or lecture notes.

All calculations run entirely in your browser. No data is sent to a server, no sign-up is required, and the tool is GDPR compliant.

What is differentiation?

Differentiation measures the rate of change of a function. Geometrically, the derivative f'(x) at a point gives the slope of the tangent line to the graph of y = f(x) at that point. Formally:

f'(x) = lim_h→0 [ f(x + h) − f(x) ] / h

In practice we rarely compute this limit directly. Instead, we apply a small set of differentiation rules that have been derived from the definition once and for all.

Standard differentiation rules

Constant rule: d/dx [k] = 0
Power rule: d/dx [xⁿ] = n·xⁿ⁻¹
Sum / difference rule: d/dx [f ± g] = f' ± g'
Constant-multiple rule: d/dx [k·f] = k·f'
Product rule: d/dx [f·g] = f'·g + f·g'
Quotient rule: d/dx [f/g] = (f'·g − f·g') / g²
Chain rule: d/dx [f(g(x))] = f'(g(x)) · g'(x)
Trig rules: d/dx [sin(x)] = cos(x), d/dx [cos(x)] = −sin(x), d/dx [tan(x)] = sec²(x)
Exponential rules: d/dx [e^x] = e^x and d/dx [a^x] = a^x·ln(a)
Logarithm rules: d/dx [ln(x)] = 1/x and d/dx [log₁₀(x)] = 1/(x·ln(10))

How to use this calculator

Type or click your function using the keyboard above. Use x as the variable, ^ for powers and standard operators.
Press Differentiate. The big result panel shows the symbolic derivative plus a breakdown of every rule applied.
(Optional) Type a value into "Slope at x =" to see the numeric value of f'(x₀). This is the slope of the tangent line at x = x₀ — useful for tangent-line problems and gradient-at-a-point questions.
Try the example chips to see how common derivatives are computed — polynomials, products, quotients, chain compositions and trig.

Common uses

GCSE Further Maths, A-Level Maths and IB HL homework
Leaving Certificate higher-level calculus problems
First-year university calculus (engineering, physics, economics, computer science)
Tangent-line, normal-line and rate-of-change problems
Optimisation: locating critical points by setting f'(x) = 0
Curve sketching and stationary-point analysis

Frequently Asked Questions

Why is my answer not fully simplified? The calculator applies differentiation rules faithfully and does only light algebraic simplification on purpose — leaving the structure visible makes it easier to see which rule produced which term. Simplify further by hand or paste the result into the Algebra Calculator.

Can I differentiate with respect to a variable other than x? The calculator uses x as the variable. If your problem uses a different letter (t, θ, …), mentally substitute it for x before entering. The structure of the answer is the same.

What does it mean when the derivative equals zero? A point where f'(x) = 0 is a stationary point: a candidate for a local maximum, local minimum or point of inflection. The second derivative — or a sign-change check on f' — tells you which.

Does it support implicit differentiation? Not yet — this tool computes explicit derivatives of one-variable functions. For implicit problems like x² + y² = 1, differentiate both sides by hand and rearrange.

Does it handle constants like π and e? Yes. Type pi or click the π key for π, and e for Euler's number. They differentiate to 0 (they are constants).

How accurate is the numeric value at a point? The symbolic derivative is exact, so f'(x₀) is evaluated using double-precision floating-point arithmetic, accurate to about 12–13 decimal places.

Is my data stored anywhere? No. Every calculation runs locally in your browser and nothing is uploaded.

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Important Note: This tool is intended to provide estimates and step-by-step educational explanations and should not be used as a substitute for professional advice. Information generated by these calculators may be incomplete and does not account for all individual circumstances. Always seek the counsel of a certified expert (such as a financial advisor, healthcare provider, or licensed engineer) before taking action based on these results.

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