What is the tangent of y=(3x+1)/(x^2+1),(1,2) ?

The tangent of y=(3x+1)/(x^2+1),(1,2) is y=-1/2 x+5/2

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tangent of y=(3x+1)/(x^2+1),(1,2)

tangent of

y = \frac{3 x + 1}{x ^{2} + 1}, (1, 2)

y = - \frac{1}{2} x + \frac{5}{2}

Solution steps

Find the slope of

y = \frac{3 x + 1}{x ^{2} + 1} : \frac{d y}{d x} = \frac{- 3 x ^{2} - 2 x + 3}{( x ^{2} + 1 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(1, 2) : y = - \frac{1}{2} x + \frac{5}{2}

y = - \frac{1}{2} x + \frac{5}{2}

y = x^{2} - 3 x, y = 5 x

y^{^{'}} = 5 y + y^{5}, y (0) = 1

x \to 2 - lim (x^{2} + 3 x)

\int x - \frac{1}{2} x + \frac{2}{x} d x

\int sec (\frac{1}{2}) x tan (\frac{1}{2}) x d x

What is the tangent of y=(3x+1)/(x^2+1),(1,2) ?
The tangent of y=(3x+1)/(x^2+1),(1,2) is y=-1/2 x+5/2