Answer: The derivative would be [tex]f'(x)=2(e^{2x}-e^{-2x})[/tex]
Step-by-step explanation:
Since we have given that
[tex]f(x)=(e^x+e^{-x})^{\frac{4}{2}}\\\\f(x)=(e^x+e^{-x})^2[/tex]
As we will use "Chain Rule"
and at last we will use the identity ''[tex]a^2-b^2=(a-b)(a+b)[/tex]''
We need to find the derivative of the function:
[tex]f'(x)=2(e^x+e^{-x})(e^x-e^{-x})\\\\f'(x)=2(e^{2x}-e^{-2x})[/tex]
Hence, the derivative would be
[tex]f'(x)=2(e^{2x}-e^{-2x})[/tex]
