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Derivative Calculator com Passos Explicativos

Gratuito · Privado · Roda no seu navegador — sem necessidade de cadastro

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 Derivada
Teclado Matemático
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Digite a expressão e pressione Ir

O Poder das Derivadas: Taxas de Variação

Determine exatamente como qualquer função se altera num único ponto.

A Regra da Potência

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

A regra fundamental para funções polinomiais.

Regras Trigonométricas

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

Essencial para modelar ondas.

Exponenciais

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

A base dos modelos de crescimento.

Como a Mudança Ocorre

A diferenciação é a espinha dorsal de qualquer rotina de otimização no aprendizado de máquina e além.

Perguntas Frequentes

Lida com derivadas secundárias e terciárias?

Sim! Você pode calcular ordens superiores.

Os resultados são precisos e perfeitos?

O motor algébrico fornece a precisão simbólica exata e confiável.

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.