1. ## derivative problem

Find the derivative of

(1+x) ^ 1/x

can anyone help me

2. Originally Posted by bwong890
Find the derivative of

(1+x) ^ 1/x

can anyone help me

$\displaystyle (1+x)^{1/x}=e^{\frac{1}{x}\ln(1+x)}$ , and now apply the chain rule here...

Tonio

3. i dont understand how you got that.

can you write it out in steps please

4. Originally Posted by bwong890
Find the derivative of

(1+x) ^ 1/x

can anyone help me
logarithmic differentiation ...

$\displaystyle y = (1+x)^{\frac{1}{x}}$

$\displaystyle \ln{y} = \frac{1}{x} \ln(1+x)$

$\displaystyle \frac{y'}{y} = \frac{1}{x} \cdot \frac{1}{1+x} - \ln(1+x) \cdot \frac{1}{x^2}$

$\displaystyle \frac{y'}{y} = \frac{1}{x}\left(\frac{1}{1+x} - \frac{\ln(1+x)}{x}\right)$

$\displaystyle y' = \frac{(1+x)^{\frac{1}{x}}}{x}\left(\frac{1}{1+x} - \frac{\ln(1+x)}{x}\right)$

5. Originally Posted by bwong890
i dont understand how you got that.

can you write it out in steps please

For all $\displaystyle a>0\,,\,\,a^x=e^{x\ln a}$ . This follows at once from the very definition of logarithm