# How do you find the derivative of #y=e^x cos(x)# ?

##### 2 Answers

This is a type of problem involving the product rule.

The product rule states:

#d/dx[f(x) * g(x)] = f'(x)g(x) + f(x)g'(x)#

So, we will let

We know that the derivative of

(if these identities look unfamiliar to you, I may recommend viewing videos from this page or this page, which explain the derivative rules for

Therefore,

#d/dx[e^x cos x] = e^x * (-sin x) + e^x * cos x#

To make this equation a little prettier, we will factor the

#d/dx[e^x cos x] = e^x * (cos x - sin x)#

#### Explanation:

When two variables are multiplied in derivative

We Have Formula,

Question: To find the derivative of

Diffentiating both side by

We get :

Here,

Which is required solution.