Question

Derivative of x^2 •root x

Answer 1

Y= x².√x

y =x².(x)¹/² → y = x²⁺¹/² → y = x⁵/²

Remember that the derivative of y = xⁿ is y' = n. xⁿ⁻¹

y = x⁵/² → y' = (5/2).x⁽⁵/²⁾⁻¹ → y' = (5/2)x³/² or y' = (5/2)√x³ or y' = (5/2)x√x

Answer 2

= x^2 * x^1/2
= x^(5/2)

derivative =  (5/2) x ^(5/2 - 1)  =  (5/2) x^(3/2)   or (5/2)(sqrt x)^3