What's the derivative of $\displaystyle \displaystyle {3x^2\frac{d^2y}{dx^2}$ with respect to x? I don't know what to make of the $\displaystyle \dfrac{d^2y}{dx^2}$. Can I say $\displaystyle \frac{d}{dx}(\frac{d^2y}{dx^2}) = \frac{d^3y}{dx^3}$?

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- Sep 29th 2010, 06:30 AMHardworkDerivative
What's the derivative of $\displaystyle \displaystyle {3x^2\frac{d^2y}{dx^2}$ with respect to x? I don't know what to make of the $\displaystyle \dfrac{d^2y}{dx^2}$. Can I say $\displaystyle \frac{d}{dx}(\frac{d^2y}{dx^2}) = \frac{d^3y}{dx^3}$?

- Sep 29th 2010, 06:39 AMProve It
You will need to use the product rule. And yes, $\displaystyle \frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) = \frac{d^3y}{dx^3}$.

- Sep 29th 2010, 06:45 AMHardwork
- Sep 29th 2010, 06:46 AMProve It
The derivative of the second derivative is the third derivative.

- Sep 29th 2010, 06:51 AMHardwork