Question

How do you find the derivative of `g(t) = (e^-t + e^t)^3`?

Answer 1

`(dg)/(dt)=3(e^(-t)+e^t)^2(e^t-e^(-t))`

Explanation:

We use the concept of function of a function. Let `g(t)=(h(t))^3`, where `h(t)=e^(-t)+e^t`

then `(dg)/(dt)=(dg)/(dh)*(dh)/(dt)`

As `g(t)=(h(t))^3`, `(dg)/(dh)=3(h(t))^2`

and as `h(t)=e^(-t)+e^t`, `(dh)/(dt)=-e^(-t)+e^t=e^t-e^(-t)`

Hence `(dg)/(dt)=3(e^(-t)+e^t)^2(e^t-e^(-t))`