# Calculate: (d)/(dx) e^x cos(x) xdx

Calculate:
$\frac{d}{dx}{e}^{x}\mathrm{cos}x$
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Pignatpmv
Use Product Rule to find the derivative of ${e}^{x}\mathrm{cos}x$. The product rule states that $\left(fg\right)\prime =f\prime g+fg\prime$
$\left(\frac{d}{dx}{e}^{x}\right)\mathrm{cos}x+{e}^{x}\left(\frac{d}{dx}\mathrm{cos}x\right)$
The derivative of ${e}^{x}$ is ${e}^{x}$.
${e}^{x}\mathrm{cos}x+{e}^{x}\left(\frac{d}{dx}\mathrm{cos}x\right)$
Use Trigonometric Differentiation: the derivative of $\mathrm{cos}x$ is - $\mathrm{sin}x$
${e}^{x}\mathrm{cos}x-{e}^{x}\mathrm{sin}x$