If xy-5=x^3/2 determine dy/dx

We have to find dy/dx.

Now we
are given that : xy - 5 = x^(3/2)

Differentiate both the
sides with respect to x

=> d/dx (xy - 5) = d/dx(
x^(3/2))

=> d/dx (xy) - d/dx(5) = d/dx(
x^(3/2))

=> x*(dy/dx) + y - 0 = 3/2 *
x^(1/2)

=> x*(dy/dx) = 3/2 * x^(1/2) -
y

=> dy/dx = (3/2)*(1/x)* x^(1/2) -
y/x

=> dy/dx = (3/2)*(x^-1/2) -
y/x

Therefore dy/dx = (3/2)*(x^-1/2) -
y/x.