Derivada de e^(7x)*cos(5x)

Answer

-\frac{5 \cdot 325368125^{7 \cdot x} \cdot \mathrm{sin}\left(5 \cdot x\right)}{119696244^{7 \cdot x}}+\frac{7 \cdot 325368125^{7 \cdot x} \cdot \mathrm{cos}\left(5 \cdot x\right)}{119696244^{7 \cdot x}}

Derivative of e^(7x)*cos(5x)

Rule Used: Product Rule
Steps: Identify a product of two functions of x in $e^{7 \cdot x}$ * $\cos(5 \cdot x)$ : use the product rule (uv)' = u'v + uv'. Each factor is differentiated once while the other is held as-is, then the two terms are added.
Differentiate each factor and combine.
Final answer: - $5 \cdot e^{7 \cdot x}$ * $\sin(5 \cdot x)$ + $7 \cdot e^{7 \cdot x}$ * $\cos(5 \cdot x)$

A derivada de e^(7*x)*cos(5*x) é -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x).

Solução passo a passo instantânea para e^(7x)*cos(5x)

Derivative ExponentialIntermediate

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Derivative of e^(7x)*cos(5x) = -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-e-minus-to-minus-the-minus-7xcos5x

Como encontrar a derivada de e^(7x)*cos(5x)

Para encontrar a derivada de e^(7x)*cos(5x), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.

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Frequently Asked Questions

What is the derivative of e^(7x)*cos(5x)?▼

The derivative of e^(7x)*cos(5x) is -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x).

How do you find the derivative of e^(7x)*cos(5x)?▼

Apply the standard differentiation rules — the key rule used here is the Product Rule. The step-by-step result is -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x).

Why is the derivative of e^(7x)*cos(5x) equal to -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x)?▼

Because differentiation measures how a function changes — applying the rules to e^(7x)*cos(5x) yields -5*e^(7*x)*sin(5*x)+7*e^(7*x)*cos(5*x). See the full step-by-step breakdown above.

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