Question

The answer is supposed to be -2(e^x - e^-x)/(e^x + e^-x)^2 but I’m not sure how to get there because my answer always ends up as -2(e^x + e^-x)/(e^x+e^x)^2, so I’m not sure where I’m missing the negative or if the answer key has a typo.

Answer 1

The answer to your question is below

Explanation:

Derivative of a quotient

`(df(x))/(dg(x)) = (f'(x)g(x) - g'(x)f(x))/(g^(2)(x) )`

f'(x) = 0

g'(x) =
`e^(x) - e^(-x)`

g²(x) = (
`(e^(x) + e^(-x) )^(2)`

Substitution

`(df(x))/(dg(x)) = (0(e^(x) + e^(-x)) - 2(e^(x)- e^(-x)))/((e^(x)+ e^(-x))^(2)  )`

Simplification and result

`(df(x))/(dg(x)) = (-2(e^(x) - e^(-x)))/((e^(x)+ e^(-x) )^(2)  )`