Answer:
a)[tex]y=\frac{4x}{x-5}[/tex]
b) [tex]\frac{dy}{dx} =\frac{-(y-4)}{x-5}[/tex]
Step-by-step explanation:
Step 1:-
Given 4x+5y = x y .......(1)
subtracting '5y' on both sides, we get
4x+5y-5y = x y - 5y
on simplification, we get
4x = y(x-5)
Dividing 'x-5' on both sides, we get
[tex]y=\frac{4x}{x-5}[/tex]
Step 2:-
by using derivative formulas
[tex]\frac{dx^{n} }{dx} = n x^{n-1}[/tex]
apply '[tex]\frac{d}{dx} (UV)= U\frac{dV}{dx} +V\frac{dU}{dx}[/tex]
Differentiating equation (1) with respective to 'x' we get
[tex]4+5\frac{dy}{dx} = x\frac{dy}{dx} +y(1)[/tex]
On simplification , taking common [tex]\frac{dy}{dx}[/tex]we get,
[tex]5\frac{dy}{dx} -x\frac{dy}{dx} =y-4[/tex]
[tex]\frac{dy}{dx} =\frac{-(y-4)}{x-5}[/tex]
