How do you find the derivative of f(x)=(x+3)/(x-3)f(x)=x+3x−3?
2 Answers
Feb 2, 2016
Using the quotient rule we have that
Feb 2, 2016
-6/(x - 3 )^2
Explanation:
differentiate using the
color(blue)(" quotient rule ") for a rational function
f(x) = g(x)/(h(x)) then:
f'(x) = (h(x).g'(x) - g(x).h'(x))/[h(x) ]^2 applying this to the above function gives :
d/dx(( x+3)/(x-3)) =( (x-3) d/dx(x+3) - (x+3) d/dx (x-3))/(x-3)^2
=( (x-3).1 - (x+3).1)/(x-3)^2 =( x-3 - x - 3)/(x-3)^2
= -6/(x-3)^2