# Math Help - Derivative of x raised to a function

1. ## Derivative of x raised to a function

Differentiate:

$y=x^ {2-X}$

2. Originally Posted by ahhh
Differentiate:

$y=x^ {2-X}$
Here's a start (assuming you're familiar with implicit differentiation):

$y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x}$.

3. $y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x}
$

Ohhhh...how can you tell when you need to use logarithmic differentation?

I understand the process now. Thanks!!

4. Originally Posted by ahhh
$y = x^{2 - x} \Rightarrow \ln y = (2 - x) \ln (x) \Rightarrow \frac{1}{y} \frac{dy}{dx} = - \ln (x) + \frac{2-x}{x}$ $
$

Ohhhh...how can you tell when you need to use logarithmic differentation?

I understand the process now. Thanks!!

$y = f(x)^{g(x)}$ is always a typical candidate.