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differentiate. y = 18\\sqrt{x} \\frac{d}{dx}(18\\sqrt{x}) = \\square

Question

differentiate. y = 18\sqrt{x}
\frac{d}{dx}(18\sqrt{x}) = \square

Explanation:

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

$9x^{-\frac{1}{2}}=\frac{9}{\sqrt{x}}$

Answer:

$\frac{9}{\sqrt{x}}$