Calculate:

$\frac{d}{dx}{e}^{x}\mathrm{cos}x$

$\frac{d}{dx}{e}^{x}\mathrm{cos}x$

inurbandojoa
2022-11-21
Answered

Calculate:

$\frac{d}{dx}{e}^{x}\mathrm{cos}x$

$\frac{d}{dx}{e}^{x}\mathrm{cos}x$

You can still ask an expert for help

Pignatpmv

Answered 2022-11-22
Author has **22** answers

Use Product Rule to find the derivative of ${e}^{x}\mathrm{cos}x$. The product rule states that $(fg)\prime =f\prime g+fg\prime $

$(\frac{d}{dx}{e}^{x})\mathrm{cos}x+{e}^{x}(\frac{d}{dx}\mathrm{cos}x)$

The derivative of ${e}^{x}$ is ${e}^{x}$.

${e}^{x}\mathrm{cos}x+{e}^{x}(\frac{d}{dx}\mathrm{cos}x)$

Use Trigonometric Differentiation: the derivative of $\mathrm{cos}x$ is - $\mathrm{sin}x$

${e}^{x}\mathrm{cos}x-{e}^{x}\mathrm{sin}x$

$(\frac{d}{dx}{e}^{x})\mathrm{cos}x+{e}^{x}(\frac{d}{dx}\mathrm{cos}x)$

The derivative of ${e}^{x}$ is ${e}^{x}$.

${e}^{x}\mathrm{cos}x+{e}^{x}(\frac{d}{dx}\mathrm{cos}x)$

Use Trigonometric Differentiation: the derivative of $\mathrm{cos}x$ is - $\mathrm{sin}x$

${e}^{x}\mathrm{cos}x-{e}^{x}\mathrm{sin}x$

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