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

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

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Answer 1 · 2016-06-20T09:21:35

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

Explanation:

Expressing $\frac{x}{2} = \frac{1}{2} x$ $x/2=1/2x$

now differentiate using the $power rule$ $color(blue)"power rule"$

$\frac{d}{d x} (a x^{n}) = n a x^{n - 1}$ $d/dx(ax^n)=nax^(n-1)$

$\Rightarrow \frac{d}{d x} (\frac{1}{2} x^{1}) = (1 \times \frac{1}{2}) x^{1 - 1} = \frac{1}{2} x^{0} = \frac{1}{2} \times 1 = \frac{1}{2}$ $rArrd/dx(1/2x^1)=(1xx1/2)x^(1-1)=1/2x^0=1/2xx1=1/2$

Answer 2 · 2016-06-25T02:14:50

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

Explanation:

Let $f (x) = \frac{x}{2}$ $f(x)=x/2$ . Then, through the limit definition of the derivative:

$f'(x)=lim_(hrarr0)(f(x+h)-f(x))/h=lim_(hrarr0)((x+h)/2-x/2)/h$

Multiplying the fraction by $2/2$ :

$f'(x)=lim_(hrarr0)((x+h)-x)/(2h)=lim_(hrarr0)h/(2h)=lim_(hrarr0)1/2=1/2$

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

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