# How do you find the derivative of #f(x)=(x+3)/(x-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 #