Answer:
see explanation
Step-by-step explanation:
Differentiate using the product rule
Given y = f(x)g(x), then
[tex]\frac{dy}{dx}[/tex] = f(x). g'(x) + g(x). f'(x)
here f(x) = [tex]e^{x}[/tex] ⇒ f'(x) = [tex]e^{x}[/tex]
g(x) = cosx ⇒ g'(x) = - sinx
Hence
[tex]\frac{dy}{dx}[/tex] = [tex]e^{x}[/tex](- sinx) + cosx [tex]e^{x}[/tex]
= [tex]e^{x}[/tex]cosx - [tex]e^{x}[/tex]sinx
