Question

find the partial derivative of ( x-y)/ (xy +2)​

Answer 1

$\huge{\underline{\underline{\bf{SOLUTION-}}}}$

* Explanation *

Assuming that we want to find the derivative with respect to x of xy2(assuming that y is a function of x.

First use the product rule:

dxd(xy2) = dxd(x)y2+xdxd(y2)

Now for dxd(xy2) = 1y2+x[2ydxdy]

dxd(xy2) = y2+2xydxdy

If you want to differentiate the expression with respect to t then the derivatives above are all dtd and dtdx may not be 1 .

dtd(xy2) = y2dtdx+2xydtdy

If you want the partial derivatives of the function f(x,y) = xy2 that has been answered in another answer.