# Derivative

• September 29th 2010, 06:30 AM
Hardwork
Derivative
What's the derivative of $\displaystyle {3x^2\frac{d^2y}{dx^2}$ with respect to x? I don't know what to make of the $\dfrac{d^2y}{dx^2}$. Can I say $\frac{d}{dx}(\frac{d^2y}{dx^2}) = \frac{d^3y}{dx^3}$?
• September 29th 2010, 06:39 AM
Prove It
You will need to use the product rule. And yes, $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}$.
• September 29th 2010, 06:45 AM
Hardwork
Quote:

Originally Posted by Prove It
You will need to use the product rule.

I can do that, thanks.

Quote:

And yes, $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}$.
Can I ask, why is that?
• September 29th 2010, 06:46 AM
Prove It
The derivative of the second derivative is the third derivative.
• September 29th 2010, 06:51 AM
Hardwork
Quote:

Originally Posted by Prove It
The derivative of the second derivative is the third derivative.

I have no idea as to why I didn't think of it that way.