1. ## 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 $\frac{d}{dx}(\frac{d^2y}{dx^2}) = \frac{d^3y}{dx^3}$?

2. You will need to use the product rule. And yes, $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}$.

3. Originally Posted by Prove It
You will need to use the product rule.
I can do that, thanks.

And yes, $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}$.
Can I ask, why is that?

4. The derivative of the second derivative is the third derivative.

5. 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.