Question

the expression xdy-ydx/x^2 is equal to​

Answer 1

We recall the concept of differentiation of $\frac{u}{v}$

$\frac{d\frac{u}{v} }{dx} =\frac{v \frac{du}{dx}-u\frac{dv}{dx} }{v^{2} }$

Given:

$\frac{xdy-ydx}{x^{2} }$

The expression is the same as $\frac{d\frac{y}{x} }{dx}$ using $\frac{u}{v}$ the formula of differentiation

$\frac{xdy-ydx}{x^{2} }=\frac{d\frac{y}{x} }{dx}$

$\frac{xdy-ydx}{x^{2} }$ equals differentiation of $\frac{y}{x}$

Answer 2

Given; xdy − ydx/x²

To Find; The equivalent

Solution; xdy− ydx/x²

In this, we first look at the condition given and observe if there is any pattern or formula like this. Recall the formula for differentiation of u/v

In this way, we can easily find out what the result will be

d(u/v)=vdu − udv/v²

So

d(x/y)=ydx − xdy/y²

Hence the result is d(y/x)