Question

What is the derivative of `y=(x-2)^(x+1)`?

Answer 1

`( ln(x-2) + {x+1}/{x-2}) (x-2)^{x+1}`

Explanation:

The easiest way to find the derivative is to start with `ln y`:

`ln y = (x+1) ln(x-2)`

so that, differentiating :

`1/y {dy}/{dx} = ln(x-2) + {x+1}/{x-2}`

so that

`{dy}/{dx} = ( ln(x-2) + {x+1}/{x-2}) (x-2)^{x+1}`