Mathematics: In exercise, find dy/dx implicity. x2y - xy2 = 3x

sorry i dont quite understand, were you given more information Step-by-step explanation:...

In exercise, find dy/dx implicity. x2y - xy2 = 3x

Ответ:

mayhy100

15.01.2022

Mathematics

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

Step-by-step explanation:

From the equation its is obvious that y is define as an explicit function of x, hence to solve implicitly, we differentiate each term of the equation with respect to x.

$x^{2} y-xy^{2}=3x\\$

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