What is the derivative of $\frac{x}{2}$ $x/2$ ?

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What is the derivative of $\frac{x}{2}$ $x/2$ ?

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Answer 1 · 2016-02-11T15:59:44

$\frac{1}{2}$ $1/2$

Explanation:

Just like the derivative of $5 x$ $5x$ is $5$ $5$ , we can write $\frac{x}{2}$ $x/2$ as $\frac{1}{2} x$ $1/2x$ . The derivative of $\frac{1}{2} x$ $1/2x$ is $\frac{1}{2}$ $1/2$ .

We can show this since, when differentiating, constants can be brought outside the differentiation.

Where $k$ $k$ is a constant, $\frac{d}{d x} (k x) = k \cdot \frac{d}{d x} (x) = k (1) = k$ $d/dx(kx)=k*d/dx(x)=k(1)=k$ .

Thus, $\frac{d}{d x} (\frac{1}{2} x) = \frac{1}{2} \cdot \frac{d}{d x} (x) = \frac{1}{2} (1) = \frac{1}{2}$ $d/dx(1/2x)=1/2*d/dx(x)=1/2(1)=1/2$ .

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