Question

let y=x√x then dy/dx =
1. 3/2 x√x
2. 3/2 √x
3. 3/2
4. 1/2​

Answer 1

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