Question

How do you find the derivative for `f(t)= te^(-t / 4)`?

Answer 1

`:f^' (t) = (4- t)/ (4 e ^(t/4))`

Explanation:

`f (t) = t e ^(-t/4)` , Product rule : `d/dx (fg) = f g^'+g f^'`

`:. f^' (t) = t * e ^(-t/4)*(-1/4)+ 1.e ^(-t/4)`

`:. f^' (t) = e ^(-t/4)(1- t/4)`

`:. f^' (t) = (4- t)/ (4 e ^(t/4))` [Ans]