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Derivative Calculator with Steps

Free · Private · Runs in your browser — no signup needed

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

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d/dx Derivative
Math Keyboard
Chargement du clavier…
Chargement du graphique…
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Enter expression and press Go

The Power of Derivatives: Instantaneous Rates of Change

If integration is the art of accumulation, differentiation is the art of change. A derivative measures exactly how a function f(x) changes at any single point. It provides the slope of the tangent line to the graph of the function.

The Power Rule

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

The fundamental rule for all polynomial functions.

Trig Rules

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

Essential for modeling wave forms and oscillations.

Exponentials

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

The base for all growth and decay models.

How Differentiation Works

Differentiation is vital for optimization—finding the maximum or minimum values of a function. Whether it's a structural engineer determining the maximum load or a data scientist optimizing a neural network, the derivative is the essential tool for finding the "best" possible outcome.

Frequently Asked Questions

Does this handle second and third derivatives?

Yes! You can calculate higher-order derivatives by simply applying the differentiation operator multiple times.

Are the results accurate?

Our symbolic engine uses formal algebraic rules to guarantee analytical perfection for all supported functions.

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.