What is the tangent of f(x)= x/(x^2+64) ?

The tangent of f(x)= x/(x^2+64) is y=(-a_{0}^2+64)/((a_{0)^2+64)^2}x+(2a_{0}^3)/((a_{0)^2+64)^2}

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tangent of f(x)= x/(x^2+64)

tangent of

f (x) = \frac{x}{x ^{2} + 64}

y = \frac{- a _{0}^{2} + 64}{( a _{0}^{2} + 64 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 64 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 64})

Find the slope of

f (x) = \frac{x}{x ^{2} + 64} : \frac{df ( x )}{d x} = \frac{- x ^{2} + 64}{( x ^{2} + 64 ) ^{2}}

Compute the slope of

f (x) = \frac{x}{x ^{2} + 64}

x = a_{0} : m = \frac{- a _{0}^{2} + 64}{( a _{0}^{2} + 64 ) ^{2}}

Find the line with slope m=

\frac{- a _{0}^{2} + 64}{( a _{0}^{2} + 64 ) ^{2}}

and passing through

(a_{0}, \frac{a _{0}}{a _{0}^{2} + 64}) : y = \frac{- a _{0}^{2} + 64}{( a _{0}^{2} + 64 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 64 ) ^{2}}

y = \frac{- a _{0}^{2} + 64}{( a _{0}^{2} + 64 ) ^{2}} x + \frac{2 a _{0}^{3}}{( a _{0}^{2} + 64 ) ^{2}}

\int_{0}^{1} 2 π (2 - y) (4 - 4 y^{2}) d y

y = - 2 x + 3, (0, 1)

\int x^{2} cos (a) x d x

\frac{\partial}{\partial x} (3 x e^{x y})

x + 1, 0, 0, 8

What is the tangent of f(x)= x/(x^2+64) ?
The tangent of f(x)= x/(x^2+64) is y=(-a_{0}^2+64)/((a_{0)^2+64)^2}x+(2a_{0}^3)/((a_{0)^2+64)^2}