# How to derive a number to the power x (e.g. 2^x)

1. Oct 7, 2009

### develish16

i recently started my calculus III course but i was stuck with the derivative part when i derive a real number to the power x ( like 2^x) and also when deriving x^x. does anybody have an idea or a link in which these kinds of derivatives can be solved. thanks for ur help

2. Oct 7, 2009

### HallsofIvy

Staff Emeritus
Use "logarithmic differentiation". If $y= x^x$, then $ln(y)= ln(x^x)= xln(x)$. Use the chain rule to differentiate ln(y) with respect to x (y'/y) and use the product rule on the right. Then solve for y'.

3. Oct 7, 2009

### LCKurtz

2x = ex ln(2)

4. Oct 13, 2009

### develish16

thx a lot guys that was so helpful