Question

How do you differentiate `f(x) = (sinx)/(e^(x-2)+x)` using the quotient rule?

Answer 1

`f'(x)=(e^(x-2)*cos(x)+xcos(x)-sin(x)e^(x-2)-sin(x))/(e^(x-2)+x)^2`

Explanation:

We have
`f'(x)=(cos(x)(e^(x-2)+x)-sin(x)(e^(x-2)+1))/(e^(x-2)+x)^2`
by the quotient rule