Question

find dx/dy, y = x^3/2

Answer 1

y=x^3/2

or, dy/dx=d{x^3/2}/dx

or, dy/dx=3(√x)/2

or, dx/dy=2/3(√x)

So first do dy/dx then just inverse it to get dx/dy.

Hope it helps.

Answer 2

$y = {x}^{ \frac{3}{2} } \\ \frac{dy}{dx} = \frac{3}{2} {x}^{ \frac{3}{2} - 1 } \\ \frac{dy}{dx} = \frac{3}{2} {x}^{ \frac{1}{2} } \\ \frac{dy}{dx} = \frac{3}{2} \sqrt{x} \\ \therefore \frac{dx}{dy} = \frac {2}{3\sqrt{x}}$