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

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anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0To solve this you have to apply the quotient rule: \[D _{x}\left[ \frac{ f(x) }{ g(x) } \right]=\frac{ f ^{\prime}(x)g(x)f(x)g ^{\prime}(x) }{ \left[ g(x) \right]^{2} }\] \[D _{x}\left[ \frac{ (1x) }{ (1+x) } \right]=\frac{ 1(1+x)(1x)1 }{ [1]^2 }\]This simplifies to...\[D _{x}=2\]Now we can insert our derivative and point into the pointslope form:\[yy _{1}=m \left( xx _{1} \right)\] \[3  y _{1}=2\left( 2x _{1} \right)\]...which simplifies to your solution:\[y=2x7\]I hope this helped!
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