Michael J. answered 07/02/16
Mastery of Limits, Derivatives, and Integration Techniques
You can also use logarithmic differentiation. This differentiation methods appreciates implicit differentiation.
y = x√x
Log both sides of the equation and bring down any exponent as the coefficient of the log.
ln(y) = √(x)ln(x)
ln(y) = x1/2ln(x)
Now, we can derive both sides of the equation.
y' / y = [(1/2)x-1/2ln(x) + (√(x) / x)]
Multiply both sides of the equation by y.
y' = y * [(ln(x) / 2√x) + (√(x) / x)]
As a result when substituting, we get the derivative
f'(x) = x√x * [(ln(x) / 2√x) + (√(x) / x)]
Now if you simplify, you should end up with the same result as Hassan's.