Originally Posted by

**soulmeetsbody** Hey, there I have one quick question for now.. I'm in grade 12 calc and we're doing derivatives and have learned the power rule (its a nice shortcut) and i'm having trouble with this one problem:

Write an equation of a tangent to each of the curves at the given point:

$\displaystyle y= \sqrt{3x^3}$ P(3,9)

Heres what I did:

$\displaystyle y=(3x^3)^\frac{1}{2}$

Then the derivative:

...Do I use the power rule on the inside brackets first? or distribute the 1/2 outside the brackets??

$\displaystyle y'=(9x^2)^\frac{1}{2}$

$\displaystyle y'=(3x)$

So my equation turns out to be

9x-y-18=0,

but the answer in the back of the book is 9x-2y-9=0

What am I doing wrong?