MHB *If (dy)/dx= x^2 y^2, then (d^2 y)/(dx^2 )=

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The discussion centers on finding the second derivative of the function given that the first derivative is dy/dx = x^2y^2. The user applies the product rule to derive d^2y/dx^2, resulting in the expression x^42y^3 + 2xy^2. There is some uncertainty about whether this result is correct, despite it appearing satisfactory to the user. The conversation highlights the importance of verifying calculations in calculus. Ultimately, the accuracy of the derived second derivative remains in question.
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If $\displaystyle\frac{dy}{dx}= x^2y^2$, then $\displaystyle\frac{d^2 y}{dx^2} =$

using the product rule

$\displaystyle x^22y (x^2y^2)+ 2xy^2$

$\displaystyle x^42y^3+2xy^2$

don't think this is the answer??
 
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Looks good to me. (Nod)
 
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