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Question
differentiate. y = 18\sqrt{x}
\frac{d}{dx}(18\sqrt{x}) = \square
Step1: Rewrite square - root as power
$y = 18x^{\frac{1}{2}}$
Step2: Apply power rule for differentiation
$\frac{d}{dx}(ax^n)=anx^{n - 1}$, so $\frac{d}{dx}(18x^{\frac{1}{2}})=18\times\frac{1}{2}x^{\frac{1}{2}-1}$
Step3: Simplify the expression
$9x^{-\frac{1}{2}}=\frac{9}{\sqrt{x}}$
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$\frac{9}{\sqrt{x}}$