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Derivative Calculator mit Schritten

Kostenlos · Privat · Läuft im Browser — keine Anmeldung erforderlich

Looking for related tools? Try our limit calculator with steps, our integral calculator with steps, or our multiple integral calculator.

Kein Backend⚡ Web-Worker
d/dx Ableitung
Mathematische Tastatur
Chargement du clavier…
Chargement du graphique…
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Die Kraft der Ableitungen: Momentane Änderungsraten

Ableitung misst, wie sich eine Funktion an einem Punkt ändert. Sie liefert die Steigung der Tangente.

Potenzregel

ddx(xn)=n⋅xn−1\frac{d}{dx}(x^n) = n \cdot x^{n-1}

Die Grundregel für Polynomfunktionen.

Trig-Regeln

ddx(sin⁡x)=cos⁡x\frac{d}{dx}(\sin x) = \cos x

Wichtig für Wellenformen.

Exponentialregeln

ddx(ex)=ex\frac{d}{dx}(e^x) = e^x

Basis für Wachstumsmodelle.

Wie Differenzierung funktioniert

Differenzierung ist entscheidend für Optimierung – das Finden von Maxima und Minima.

Häufig gestellte Fragen

Werden zweite Ableitungen unterstützt?

Ja! Höhere Ableitungen sind durch mehrfache Anwendung möglich.

Sind die Ergebnisse genau?

Unsere Engine nutzt formale Regeln für perfekte Ergebnisse.

How do you find the derivative of a function with steps?

Identify the structure of your function and apply the corresponding differentiation rule: power rule for polynomials, exponential and logarithmic rules, trigonometric formulas, or combination rules like the product, quotient, and chain rules. Simplify algebraically at each step.

What differentiation rules does this calculator support?

Mathsway supports the Power Rule, Product Rule, Quotient Rule, Chain Rule, Trigonometric and Inverse Trigonometric rules, Exponential and Logarithmic derivatives, and implicit differentiation principles with full algebraic steps.

Can this calculator compute higher-order derivatives?

Yes. You can calculate second, third, and higher-order derivatives (f''(x), f'''(x)) by repeatedly differentiating the result step by step.

What is the Chain Rule and when do I use it?

The Chain Rule differentiates composite functions f(g(x)). It states that (f(g(x)))' = f'(g(x)) · g'(x). You differentiate the outer function evaluated at the inner function, then multiply by the derivative of the inner function.

Is this derivative calculator free and does it require signup?

Yes, it is completely free, runs directly in your browser with Web Workers, requires no account or signup, and your data remains private on your device.

How are derivatives related to limits?

The derivative is formally defined as the limit of the difference quotient as h approaches 0: f'(x) = limh→0 (f(x+h) − f(x))/h. If you need to evaluate limits directly, use our limit calculator with steps.

How are derivatives related to integrals?

By the Fundamental Theorem of Calculus, differentiation and integration are inverse operations. The derivative represents instantaneous rate of change, while the integral represents total accumulation. You can verify antiderivatives with our integral calculator with steps or explore multivariable calculus with our multiple integral calculator.