What is the answer to this calculus problem??? (d)/(dx) (e {}^(x) cos \: x) ​

Question

What is the answer to this calculus problem???


`(d)/(dx) (e {}^(x) cos \: x)`
​

Answer 1

see explanation

Explanation:

Differentiate using the product rule

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

`(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

`(dy)/(dx)` =
`e^(x)`(- sinx) + cosx
`e^(x)`

=
`e^(x)`cosx -
`e^(x)`sinx