Question

What is the answer to this calculus problem???%7Bx%7D%20cos%20%5C%3A%20x%29" id="TexFormula1" title=" \frac{d}{dx} (e {}^{x} cos \: x)" alt=" \frac{d}{dx} (e {}^{x} cos \: x)" align="absmiddle" class="latex-formula">
​

Answer 1

Answer:

see explanation

Step-by-step explanation:

Differentiate using the product rule

Given y = f(x)g(x), then

$\frac{dy}{dx}$ = f(x). g'(x) + g(x). f'(x)

here f(x) = $e^{x}$ ⇒ f'(x) = $e^{x}$

g(x) = cosx ⇒ g'(x) = - sinx

Hence

$\frac{dy}{dx}$ = $e^{x}$(- sinx) + cosx $e^{x}$

                                   = $e^{x}$cosx - $e^{x}$sinx