Question

Find an equation of the tangent line to the curve
y=(1-x)/(1+x) points (-2,-3)

Answer 1

To solve this you have to apply the quotient rule: \[D _{x}\left[ \frac{ f(x) }{ g(x) } \right]=\frac{ f ^{\prime}(x)g(x)-f(x)g ^{\prime}(x) }{ \left[ g(x) \right]^{2} }\] \[D _{x}\left[ \frac{ (1-x) }{ (1+x) } \right]=\frac{ -1(1+x)-(1-x)1 }{ [1]^2 }\]This simplifies to...\[D _{x}=-2\]Now we can insert our derivative and point into the point-slope form:\[y-y _{1}=m \left( x-x _{1} \right)\] \[-3 - y _{1}=-2\left( -2-x _{1} \right)\]...which simplifies to your solution:\[y=-2x-7\]I hope this helped!