What is the tangent of x+6/x ?

The tangent of x+6/x is y=(1-6/(a_{0)^2})x+(12)/(a_{0)}

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tangent of x+6/x

tangent of

x + \frac{6}{x}

y = (1 - \frac{6}{a _{0}^{2}}) x + \frac{12}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + \frac{6}{a _{0}})

Find the slope of

y = x + \frac{6}{x} : \frac{d y}{d x} = 1 - \frac{6}{x ^{2}}

Compute the slope of

y = x + \frac{6}{x}

x = a_{0} : m = 1 - \frac{6}{a _{0}^{2}}

Find the line with slope m=

1 - \frac{6}{a _{0}^{2}}

and passing through

(a_{0}, a_{0} + \frac{6}{a _{0}}) : y = (1 - \frac{6}{a _{0}^{2}}) x + \frac{12}{a _{0}}

y = (1 - \frac{6}{a _{0}^{2}}) x + \frac{12}{a _{0}}

\int - cos (x) d x

x^{4} sin (x) tan (x)

x \to 4 lim (\frac{x + 5 - 3}{x - 4})

\frac{d}{d x} (x^{2} n)

f (x) = 5 + 5 x^{2} - 2 x^{3}, at x = 1

What is the tangent of x+6/x ?
The tangent of x+6/x is y=(1-6/(a_{0)^2})x+(12)/(a_{0)}