What is the tangent of f(x)=(-4x)/(x^2+1),(1,2) ?

The tangent of f(x)=(-4x)/(x^2+1),(1,2) is y=2 \lor y=0.21178…x+1.78821…

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tangent of f(x)=(-4x)/(x^2+1),(1,2)

tangent of

f (x) = \frac{- 4 x}{x ^{2} + 1}, (1, 2)

y = 2 or y = 0.21178 \dots x + 1.78821 \dots

Solution steps

f (x) = \frac{- 4 x}{x ^{2} + 1} : f (x) = - \frac{4 x}{x ^{2} + 1}

Slope of the tangent line at

(1, 2) : m = \frac{- 4 x - 2 ( x ^{2} + 1 )}{( x ^{2} + 1 ) ( x - 1 )}

Find the slope of

f (x) = - \frac{4 x}{x ^{2} + 1} : m = - \frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

Solve

- \frac{4 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}} = \frac{- 4 x - 2 ( x ^{2} + 1 )}{( x ^{2} + 1 ) ( x - 1 )} : x = - 1, x \approx - 3.95137 \dots

Find the tangent line at

x = - 1 : y = 2

Find the tangent line at

x = - 3.95137 \dots : y = 0.21178 \dots x + 1.78821 \dots

y = 2 or y = 0.21178 \dots x + 1.78821 \dots

\int \frac{3}{2 x - 1} d x

y^{^{''}} + 4 y = 8 t^{2} - 20 t + 8

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}} - x + 3)

\frac{d}{d x} (\frac{5 x}{( x ^{3} - 6 ) ^{2}})

\frac{\partial}{\partial x} (\frac{3}{2 x ^{2}})

What is the tangent of f(x)=(-4x)/(x^2+1),(1,2) ?
The tangent of f(x)=(-4x)/(x^2+1),(1,2) is y=2 \lor y=0.21178…x+1.78821…