Question

How do you differentiate `(-x^2 -5x-4 )/ (2x^2-1)` using the quotient rule?

Answer 1

`(-8x^3 - 30x^2 - 14x + 5)/(2x^2 - 1 )^2`

Explanation:

Applying the quotient rule gives :

`f'(x) = (((2x^2 -1 ). d/dx(- x^2 - 5x - 4 ) - (- x^2 - 5x - 4 ).d/dx(2x^2 - 1 )))/(2x^2 -1 )^2`

`rArr f'(x) =( (2x^2 - 1 )(2x - 5 ) - (-x^2 - 5x -4)(4x))/(2x^2 - 1 )^2`

now 'tidying' the numerator ie. multiply out brackets and collect like terms :

`f'(x) =( -4x^3 +2x - 10x^2 +5 -4x^3 - 20x^2 - 16x)/(2x^2 - 1 )^2`

`rArr f'(x) = (- 8x^3 - 30x^2 - 14x + 5)/(2x^2 - 1 )^2`