How do you find the derivative of f(x)=(x+3)/(x-3)f(x)=x+3x3?

2 Answers

Using the quotient rule we have that

f'(x)=((x+3)'*(x-3)-(x-3)'*(x+3))/(x-3)^2=> f'(x)=((x-3)-(x+3))/(x-3)^2=> f'(x)=-6/(x-3)^2

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