How do you find the derivative of #y=e^x cos(x)# ?
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
#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)#
When two variables are multiplied in derivative
We Have Formula,
Question: To find the derivative of
Diffentiating both side by
We get :
Which is required solution.
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