## hawkfalcon Group Title if dy/dx =x^2 y^2 then d^2y/dx^2=? one year ago one year ago

1. hawkfalcon Group Title

So $\frac{ dy }{dx }(x^2y^2)$

2. hawkfalcon Group Title

Which I get to be -2x^2y/2xy^2 but thats not an option...

3. wio Group Title

$\Large \begin{array}{rcl} \frac{dx}{dx} &=&x^2 y^2 \\ \frac{dx}{dx} \left(\frac{dx}{dx}\right) &=& \frac{dx}{dx} (x^2 y^2) \\ \frac{d^2y}{dx^2} &=& (2x)y^2 + x^2\left (2y\frac{dy}{dx} \right) \\ \frac{d^2y}{dx^2} &=& 2xy^2 + 2x^2y(x^2y^2 ) \\ \frac{d^2y}{dx^2} &=& 2xy^2 + 2x^4y^3 \end{array}$

4. hawkfalcon Group Title

Oh so I can replace dy/dx with the original function?

5. hawkfalcon Group Title

Cool! Thanks!

6. wio Group Title

In general, when you have an equation, the left and side and right hand side can always be substituted. The exception is when you're trying to prove the equation is true.