# How do you find the instantaneous rate of change of the function #f(x)=x/(x+2)# when x=2?

##### 1 Answer

Feb 7, 2016

#### Explanation:

The instantaneous rate of change at

To find the derivative, use the quotient rule, which states that

#d/dx[g(x)/(h(x))]=(g'(x)h(x)-g(x)h'(x))/[h(x)]^2#

Applying this to the function at hand, we see that

#f'(x)=((x+2)d/dx[x]-xd/dx[x+2])/(x+2)^2#

Note that both of these derivatives are equal to

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

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

#f'(x)=2/(x+2)^2#

The instantaneous rate of change at

#f'(2)=2/(2+2)^2=2/4^2=2/16=1/8#