What is the tangent of y= 4/x ?

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

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tangent of y= 4/x

tangent of

y = \frac{4}{x}

y = - \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}, \frac{4}{a _{0}})

Find the slope of

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

Compute the slope of

y = \frac{4}{x}

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

Find the line with slope m=

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

and passing through

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

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

\int_{2}^{8} \frac{1}{x ^{2} - 1} d x

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

x^{2} \cdot cos (x)

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

\frac{d}{d x} (\frac{2}{x ^{2} + 7})

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