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

1 Answer
Jun 2, 2016

#(-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#