# Differentiation Question Concerning natural log

1. Jan 19, 2005

Hello all

If $$y = e^3^\ln^(x^2)$$ find $$\frac {dy}{dx}$$

So $$\frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2)$$

So the simplified answer is: $$\frac {6}{x} e^3^\ln^(x^2)$$

Is this correct? IS there any other way of expressing the answer?

Thanks

2. Jan 19, 2005

### chroot

Staff Emeritus
Use your log rules.

$$e^{3 \ln x^2} \equiv e^{\ln x^6} \equiv x^6$$

- Warren

3. Jan 19, 2005

oh i see

So derivative would be $$6x^5$$

didn't catch that

thanks

4. Jan 19, 2005

### chroot

Staff Emeritus
Pretty much anytime you see e and ln stuck together like that, it means your teacher is trying to get you to use log rules.

- Warren