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**

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)**

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.

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