Question

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

Answer 1

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

Step-by-step explanation:

Since we have given that

$f(x)=(e^x+e^{-x})^{\frac{4}{2}}\\\\f(x)=(e^x+e^{-x})^2$

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

$f'(x)=2(e^{2x}-e^{-2x})$