# How do you find the derivative of #f(x)=(3+x)/(1-3x)#?

##### 2 Answers

Mar 3, 2016

#### Explanation:

Separate the top and the bottom into f and g then find the derivatives of each of them and then put it into the quotient rule

Mar 3, 2016

#### Explanation:

differentiate using the

#color(blue)" Quotient rule " # If f(x)

#= g(x)/(h(x) )" then " f'(x) =( g(x).h'(x) - h(x).g'(x))/(h(x))^2 # here : g(x) = 3+x

# " and " g'(x) = 1 # and

# h(x) = 1 - 3x" and " h'(x) = -3 # substituting these results into f'(x)

#f'(x) =( (3+x)(-3) - (1-3x).1)/(1-3x)^2 #

#= (-9-3x-1+3x)/(1-3x)^2 = -10/(1-3x)^2#