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How to differentiate y=x/square root x?

1 Answer

Jun 18, 2018

$\frac{d y}{d x} = \frac{1}{2 \sqrt{x}}$ $dy/dx =1/(2sqrtx)$

Explanation:

$y = \frac{x}{\sqrt{x}}$ $y = x/sqrtx$

$= x \times x^{- \frac{1}{2}} = x^{\frac{1}{2}}$ $= x xx x^(-1/2) = x^(1/2)$

Apply power rule

$\frac{d y}{d x} = \frac{1}{2} x^{\frac{1}{2} - 1}$ $dy/dx = 1/2 x^(1/2-1)$

$= \frac{1}{2} x^{- \frac{1}{2}}$ $= 1/2 x^(-1/2)$

$= \frac{1}{2 \sqrt{x}}$ $= 1/(2sqrtx)$

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