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

Question

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

1 Answer

Impact of this question

5095 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-22T07:19:13

$\frac{d y}{d x} = \frac{- (5 x + 3 x y^{2})}{3 y (x^{2} + y)}$ $(dy)/(dx)=(-(5x+3xy^2))/(3y(x^2+y)$

Explanation:

we want

$\frac{d}{d x} (- 3 x^{2} y^{2}) - \frac{d}{d x} (2 y^{3}) + \frac{d}{d x} (5) = \frac{d}{d x} (5 x^{2})$ $d/(dx)(-3x^2y^2)-d/(dx)(2y^3)+d/(dx)(5)=d/(dx)(5x^2)$

We will differentiate implicitly.

The first term will also need the product rule

$\frac{d}{d x} (u v) = v \frac{d u}{d x} + u \frac{d v}{d x}$ $color(red)(d/(dx)(uv)=v(du)/(dx)+u(dv)/(dx))$

$y^{2} (- 6 x) + (- 3 x^{2}) 2 y \frac{d y}{d x} - 6 y^{2} \frac{d y}{d x} + 0 = 10 x$ $y^2(-6x)+(-3x^2)2y(dy)/(dx)-6y^2(dy)/(dx)+0=10x$

$- 6 x y^{2} - 6 x^{2} y \frac{d y}{d x} - 6 y^{2} \frac{d y}{d x} = 10 x$ $-6xy^2-6x^2y(dy)/(dx)-6y^2(dy)/(dx)=10x$

now rearrange for $\frac{d y}{d x}$ $(dy)/(dx)$ and tidy up.

$\frac{d y}{d x} (- 6 x^{2} y - 6 y^{2}) = 10 x + 6 x y^{2}$ $(dy)/(dx)(-6x^2y-6y^2)=10x+6xy^2$

$\frac{d y}{d x} = \frac{10 x + 6 x y^{2}}{- 6 y (x^{2} + y)}$ $(dy)/(dx)=(10x+6xy^2)/(-6y(x^2+y)$

$\frac{d y}{d x} = \frac{- (5 x + 3 x y^{2})}{3 y (x^{2} + y)}$ $(dy)/(dx)=(-(5x+3xy^2))/(3y(x^2+y)$

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find (dy)/(dx)dydx(dy)/(dx) given -3x^2y^2-2y^3+5=5x^2−3x2y2−2y3+5=5x2-3x^2y^2-2y^3+5=5x^2?

1 Answer

Explanation:

Related questions

Impact of this question

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