Question

What is the derivative of `x*x^(1/2)`?

Answer 1

The derivative is `3/2sqrt(x)`.

Explanation:

`x * x^(1/2) = x^(1+ 1/2) = x^(2/2 + 1/2) = x^(3/2)`.

The power rule states that `d/dx(x^n) = nx^(n - 1)`

`d/dx(x^(3/2)) = 3/2x^(1/2) = 3/2sqrt(x)`