What is the tangent of x+4/x ?

The tangent of x+4/x is y=(1-4/(a_{0)^2})x+8/(a_{0)}

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tangent of x+4/x

tangent of

x + \frac{4}{x}

y = (1 - \frac{4}{a _{0}^{2}}) x + \frac{8}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + \frac{4}{a _{0}})

Find the slope of

y = x + \frac{4}{x} : \frac{d y}{d x} = 1 - \frac{4}{x ^{2}}

Compute the slope of

y = x + \frac{4}{x}

x = a_{0} : m = 1 - \frac{4}{a _{0}^{2}}

Find the line with slope m=

1 - \frac{4}{a _{0}^{2}}

and passing through

(a_{0}, a_{0} + \frac{4}{a _{0}}) : y = (1 - \frac{4}{a _{0}^{2}}) x + \frac{8}{a _{0}}

y = (1 - \frac{4}{a _{0}^{2}}) x + \frac{8}{a _{0}}

\frac{d}{d y} (\frac{y ^{4}}{4} + \frac{1}{8 y ^{2}})

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

\int 2 x^{\frac{1}{4}} - 3 x^{3} d x

\frac{d}{d θ} (14 sin (θ))

\frac{d y}{d x} = 2 x e^{- y}

What is the tangent of x+4/x ?
The tangent of x+4/x is y=(1-4/(a_{0)^2})x+8/(a_{0)}