Michael J. answered • 07/02/16

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Mastery of Limits, Derivatives, and Integration Techniques

You can also use logarithmic differentiation. This differentiation methods appreciates implicit differentiation.

Let y=f(x)

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) = x

^{1/2}ln(x)Now, we can derive both sides of the equation.

y' / y =

**[**(1/2)x^{-1/2}ln(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.

Hassan O.

07/02/16