Answer:
The answer to your question is below
Step-by-step explanation:
Derivative of a quotient
[tex]\frac{df(x)}{dg(x)} = \frac{f'(x)g(x) - g'(x)f(x)}{g^{2}(x) }[/tex]
f'(x) = 0
g'(x) = [tex]e^{x} - e^{-x}[/tex]
g²(x) = ([tex](e^{x} + e^{-x} )^{2}[/tex]
Substitution
[tex]\frac{df(x)}{dg(x)} = \frac{0(e^{x} + e^{-x)} - 2(e^{x}- e^{-x)}}{(e^{x}+ e^{-x})^{2} }[/tex]
Simplification and result
[tex]\frac{df(x)}{dg(x)} = \frac{-2(e^{x} - e^{-x})}{(e^{x}+ e^{-x} )^{2} }[/tex]
