# Math Help - Derivative

1. ## Derivative

I'm sure I am making a simple mistake...

Find the derivative of the following $\frac {-2x}{6y^2}$

(the question actually asks for the second derivative, the equation above is the first derivative... I'm just not sure how to take the 2nd derivative).

2. Do you need to find the derivative implicitly? This means for either x or y. Or are you looking for parital derivatives?

3. Originally Posted by jhb
I'm sure I am making a simple mistake...

Find the derivative of the following $\frac {-2x}{6y^2}$

(the question actually asks for the second derivative, the equation above is the first derivative... I'm just not sure how to take the 2nd derivative).

Hopefully you're differentiating with respect to x.
$\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{-2x}{6y^2}\right)=\frac{6y^2(-2)+2x(6)\cdot2y\frac{dy}{dx}}{(6y^2)^2}$

I think that you'll see here that you can simplify matters by substitution...

4. Yeah, sorry. The question states: Using implicit differentiation, find the second derivative

Original Equation:

For the first derivative, I got: $\frac {-2x}{6y^2}$

5. Originally Posted by jhb
Yeah, sorry. The question states: Using implicit differentiation, find the second derivative

Original Equation:

For the first derivative, I got: $\frac {-2x}{6y^2}$
in future, post the entire problem to avoid confusion.

$y' = -\frac{x}{3y^2}$

$y'' = -\frac{3y^2 - 6xy \cdot y'}{9y^4}$

$y'' = -\frac{3y^2 - 6xy \cdot \left(-\frac{x}{3y^2}\right)}{9y^4}
$

clean up the algebra