Question

How do you find the derivative of `x / 2`?

Answer 1

`1/2`

Explanation:

Expressing `x/2=1/2x`

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

`d/dx(ax^n)=nax^(n-1)`

`rArrd/dx(1/2x^1)=(1xx1/2)x^(1-1)=1/2x^0=1/2xx1=1/2`

Answer 2

`1/2`

Explanation:

Let `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`