Question

How do you differentiate `f(x)= (x+5)/ (2x-7 )` using the quotient rule?

Answer 1

`(-17)/(2x-7)^2`

Explanation:

differentiate using the `color(blue)"quotient rule"`

f(x) `=(g(x))/((h(x))) "then " f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x)^2`
`"-----------------------------------------------------------------------"`
g(x) = x + 5 → g'(x) = 1

h(x) 2x - 7 → h'(x) = 2
`"---------------------------------------------------------------------"`
Substitute these values into f'(x)

`f'(x)=((2x-7).1-(x+5).2)/(2x-7)^2`

`=(2x-7-2x-10)/(2x-7)^2=(-17)/(2x-7)^2`