If xy5x32 determine dydx If xy5x32 determine dydxSolutionFor

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

For xy - 5 = x^(3/2) the value of dy/dx can be found using implicit differentiation.

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

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

xy - 5 = x^(3/2)

=> y = (x^(3/2) + 5)/x

dy/dx = ((3/2)*x^(1/2) - (x^(3/2) + 5)/x)/x

The required derivative dy/dx = ((3/2)*x^(1/2) - (x^(3/2) + 5)/x)/x