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

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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**

this is your final answer you can also do this by the help of an implicit differentiation calculator this will also show you the steps involved in solving these.

To differentiate x wtih respect to y, dy/dx, we'll have to find a function of x.

xy-5=x^3/2

We'll add 5 both sides:

xy = x^3/2 + 5

y = [x^(3/2) + 5]/x

Now, we'll differentiate both sides:

dy/dx = {(d/dx)[x^(3/2) + 5]*x - [x^(3/2) + 5]*(d/dx)(x)}/x^2

dy/dx = [(3/2)*xsqrtx - xsqrtx - 5]/x^2

We'll combine like terms from numerator:

**dy/dx = (xsqrtx - 10)/2x^2**

**dy/dx = sqrtx/2x - (5/x^2)**