# Thread: Derivative of x raised to a function

1. ## Derivative of x raised to a function

Differentiate:

$\displaystyle y=x^ {2-X}$

2. Originally Posted by ahhh
Differentiate:

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

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

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

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

I understand the process now. Thanks!!

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

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

I understand the process now. Thanks!!

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