Derivative Help

Question

solve f(x)=e^(sin5x)

 

The answer is (5e^(sin5x))(cos5x)

 

I dont understand how the 5 ended up in front of e

 

Thankyou for the help

Answer 1

f(x) = e^sin(5x)

 

Use the chain rule.

 

f'(x) = e^sin(5x) d/dx [sin(5x)]

 

d/dx [sin(5x)] = 5cos(5x)

 

f'(x) = e^sin(5x) [5cos(5x)] = 5 e^sin(5x) cos(5x)