Question

How do you find the derivative of `1/(2x)`?

Answer 1

`-1/(2x^2)`

Explanation:

Differentiate using the `color(blue)"power rule"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(a/a)|)))`

Rewrite the function as.

`1/(2x)=1/2xx1/x=1/2xxx^-1=1/2x^-1`

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

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

Answer 2

ALTERNATIVE APPROACH

Explanation:

By the quotient rule:

`(1/(2x))' = ((0 xx 2x) - (1 xx 2))/(2x)^2`

`(1/(2x))' = -2/(4x^2)`

`(1/(2x))' = -1/(2x^2)`

Hopefully this helps!