What is the tangent of y=(5x)/(1+x^2),(5, 25/26) ?

The tangent of y=(5x)/(1+x^2),(5, 25/26) is y=-30/169 x+625/338

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tangent of y=(5x)/(1+x^2),(5, 25/26)

tangent of

y = \frac{5 x}{1 + x ^{2}}, (5, \frac{25}{26})

y = - \frac{30}{169} x + \frac{625}{338}

Solution steps

Find the slope of

y = \frac{5 x}{1 + x ^{2}} : \frac{d y}{d x} = \frac{5 ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{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{30}{169}

Find the line with slope m=

- \frac{30}{169}

and passing through

(5, \frac{25}{26}) : y = - \frac{30}{169} x + \frac{625}{338}

y = - \frac{30}{169} x + \frac{625}{338}

What is the tangent of y=(5x)/(1+x^2),(5, 25/26) ?
The tangent of y=(5x)/(1+x^2),(5, 25/26) is y=-30/169 x+625/338