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Single Variable Calculus

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Difficult

Log Differentiation with $x$ to the Power of Square Root Function

SVCALC-0CKELE

Find derivative of the function $y=x^{\sqrt{x}}$.

A

$x^{\sqrt{x}}(\cfrac{\ln(x)}{2 \sqrt{x}} +\cfrac{1}{\sqrt{x}})$

B

$\cfrac{\ln(x)}{2 \sqrt{x}} +\cfrac{1}{\sqrt{x}}$

C

$\sqrt{x}x^{\sqrt{x}-1}$

D

$x^{\sqrt{x}}$