Question

How do you differentiate `f(x)= -1 / (-2x-4 )` using the quotient rule?

Answer 1

`f'(x) = ( -2 ) / (2x+4)^2`

Explanation:

I would first remove the -ve sign as `-1` can be factored out from the denominator.

So `f(x) = -1/(-2x-4)`
`:. f(x) = 1/(2x+4)`

You need to use the quotient rule;
`d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2`
to give:

`f'(x) = { ( (2x+4)(d/dx1) - (1)(d/dx(2x+4)) ) / (2x+4)^2 }`
`:. f'(x) = ( 0 - (1)(2) ) / (2x+4)^2`
`:. f'(x) = ( -2 ) / (2x+4)^2`