## hawkfalcon 3 years ago if dy/dx =x^2 y^2 then d^2y/dx^2=?

1. hawkfalcon

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

2. hawkfalcon

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

3. anonymous

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

4. hawkfalcon

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

5. hawkfalcon

Cool! Thanks!

6. anonymous

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.