Differentiation Question Concerning natural log

[courtrigrad]

Hello all

If [tex] y = e^3^\ln^(x^2) [/tex] find [tex] \frac {dy}{dx} [/tex]

So [tex] \frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2) [/tex]

So the simplified answer is: [tex] \frac {6}{x} e^3^\ln^(x^2) [/tex]

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

Thanks

 

[chroot]

Use your log rules.

[tex]e^{3 \ln x^2} \equiv e^{\ln x^6} \equiv x^6[/tex]

- Warren

 

[courtrigrad]

oh i see

So derivative would be [tex] 6x^5 [/tex]

didn't catch that

thanks

 

[chroot]

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