How do you find the derivative of $\frac{x}{2}$ $x/2$ ?

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How do you find the derivative of $\frac{x}{2}$ $x/2$ ?

1 Answer

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Answer 1 · 2016-05-15T15:23:00

Use the facts that $\frac{x}{2} = \frac{1}{2} x$ $x/2 = 1/2 x$ and $\frac{d}{d x} (k x) = k$ $d/dx(kx)=k$ to get $\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}$ $d/dx(x/2) = 1/2$

Explanation:

$\frac{d}{d x} (\frac{x}{2}) = \frac{d}{d x} (\frac{1}{2} x) = \frac{1}{2} \frac{d}{d x} (x) = \frac{1}{2} (1) = \frac{1}{2}$ $d/dx(x/2) = d/dx(1/2x) = 1/2 d/dx(x) = 1/2 (1) = 1/2$

If you prefer to use the quotient rule it looks like this:

$\frac{d}{d x} (\frac{x}{2}) = \frac{\frac{d}{d x} (x) \cdot 2 - x \frac{d}{d x} (2)}{2^{2}}$ $d/dx(x/2) = (d/dx(x)*2-x d/dx(2))/2^2$

$= \frac{1 \cdot 2 - x \cdot (0)}{4} = \frac{2}{4} = \frac{1}{2}$ $= (1*2-x*(0))/4 = 2/4 = 1/2$

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How do you find the derivative of $\frac{x}{2}$ $x/2$ ?

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