Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

f(x) = (e^x + e^-x)4/2

Answer 1

Answer: The derivative would be
`f'(x)=2(e^(2x)-e^(-2x))`

Explanation:

Since we have given that

`f(x)=(e^x+e^(-x))^{(4)/(2)}\\\\f(x)=(e^x+e^(-x))^2`

As we will use "Chain Rule"

and at last we will use the identity ''
`a^2-b^2=(a-b)(a+b)`''

We need to find the derivative of the function:

`f'(x)=2(e^x+e^(-x))(e^x-e^(-x))\\\\f'(x)=2(e^(2x)-e^(-2x))`

Hence, the derivative would be

`f'(x)=2(e^(2x)-e^(-2x))`