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

The tangent of 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 x/(x^2+64)

tangent of

\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

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

Compute the slope of

y = \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}}

x \to 3 lim (\frac{( x ^{2} - 6 )}{( x - 9 )})

\frac{d}{d x} (lo g_{6} (3 x^{3} + 4 x^{2} + 4 x))

\int 64 - 5 x^{2} d x

\int \frac{( x ^{2} )}{20 - 4 x + x ^{2}} d x

\int \frac{ln ( 16 x )}{x} d x

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