How do you find $(dy)/(dx)$ given $-3x^2y^2-2y^3+5=5x^2$ ?

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Answer 1 · 2017-09-22T07:19:13

$(dy)/(dx)=(-(5x+3xy^2))/(3y(x^2+y)$

we want

$d/(dx)(-3x^2y^2)-d/(dx)(2y^3)+d/(dx)(5)=d/(dx)(5x^2)$

We will differentiate implicitly.

The first term will also need the product rule

$color(red)(d/(dx)(uv)=v(du)/(dx)+u(dv)/(dx))$

$y^2(-6x)+(-3x^2)2y(dy)/(dx)-6y^2(dy)/(dx)+0=10x$

$-6xy^2-6x^2y(dy)/(dx)-6y^2(dy)/(dx)=10x$

now rearrange for $(dy)/(dx)$ and tidy up.

$(dy)/(dx)(-6x^2y-6y^2)=10x+6xy^2$

$(dy)/(dx)=(10x+6xy^2)/(-6y(x^2+y)$

$(dy)/(dx)=(-(5x+3xy^2))/(3y(x^2+y)$

How do you find (dy)/(dx)(dy)/(dx) given -3x^2y^2-2y^3+5=5x^2-3x^2y^2-2y^3+5=5x^2?