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 Lommeregner

Differentier enhver funktion trin for trin. Skriv udtrykket direkte eller brug det specialiserede tastatur til trig, log, eksponentielle og potensfunktioner.

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

3x^2 + 2x - 5

Drikkepenges: powers need ^ — type x^2 for x² (bare x2 betyder x·2). Multiplikation er implicit — 2x, 3sin(x) og 5(x+1) virker alle. Brug 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

Hældning ved x =

Lad tomt for det symbolske derivat. Udfyld en værdi for også at se f'(x₀) — hældningen af tangentlinjen i det punkt.

Afledt

Om kalkulus-differentiations-lommeregneren

Calculus Derivative Calculator finder derivatet af en funktion med hensyn til x og viser arbejdet linje for linje. Den er bygget til students, educators and self-learners, der ønsker at se why et svar er korrekt, ikke blot det endelige resultat. Hvert trin navngiver den regel, der blev anvendt — potensregel, sumregel, konstantmultiplikationsregel, produktregel, kvotientregel, kæderegel, trigonometriske regler, eksponentielregel eller logaritmeregel — så du kan matche det med din lærebog eller forelæsningsnoter.

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Hvad er differentiering?

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 ved hjælp af tastaturet ovenfor. Brug x som variablen, ^ til potenser og standardoperatorer.
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 =" for at se den numeriske værdi af f'(x₀). Dette er hældningen af tangentenlinjen ved x = x₀ – nyttig til tangentproblemer og spørgsmål om gradient i et punkt.
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-kalkulus på højt niveau
Første år på universitetet i kalkulus (ingeniørvidenskab, fysik, økonomi, datalogi)
Tangent-line, normal-line and rate-of-change problems
Optimisation: locating critical points by setting f'(x) = 0
Curve sketching and stationary-point analysis

Ofte stillede spørgsmål

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? Et punkt, hvor f'(x) = 0 er en stationary point: en kandidat til et lokalt maksimum, lokalt minimum eller inflektionspunkt. Den anden afledte — eller en fortegnskontrol af f' — fortæller dig hvilken.

Does it support implicit differentiation? Ikke endnu — dette værktøj beregner explicit derivater af en-variable funktioner. For implicitte problemer som x² + y² = 1, differentiér begge sider i hånden og omform.

Does it handle constants like π and e? Ja. Skriv pi eller klik på π-tasten for π og e for Eulers tal. De differentieres til 0 (de er konstanter).

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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Vigtig bemærkning: Dette værktøj er beregnet til at give estimater og trinvise uddannelsesforklaringer og bør ikke bruges som erstatning for professionel rådgivning. Oplysninger genereret af disse lommeregnere kan være ufuldstændige og tager ikke højde for alle individuelle omstændigheder. Søg altid rådgivning fra en certificeret ekspert (som en finansiel rådgiver, sundhedsperson eller licenseret ingeniør), inden du handler baseret på disse resultater.

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