derivative of f(x)=2 cot (4e^x)

Answer 1

To find the derivative of f(x) = 2cot(4e^x), we will use the chain rule.

First, let's find the derivative of the inner function, g(x) = 4e^x:
g'(x) = 4e^x

Now, let's find the derivative of f(x) using the chain rule:
f'(x) = -2csc^2(4e^x) * (4e^x)'
= -2csc^2(4e^x) * 4e^x

Therefore, the derivative of f(x) = 2cot(4e^x) is f'(x) = -8e^x csc^2(4e^x).