# How do you find an equation of the tangent line to the curve #y=(2x)/(x+1)# at the point (1,1)?

##### 1 Answer

Feb 5, 2017

#### Explanation:

The equation of the line tangent to the curve

In our case:

#x_0 = 1#

#f(x_0) = (2*1)/(1+1) =2/2 =1#

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

#f'(x_0)= 2/(1+1)^2 = 2/2^2 = 2/4 = 1/2#

So the equation of the tangent line is: