What is the tangent of 3/x ?

The tangent of 3/x is y=-3/(a_{0)^2}x+6/(a_{0)}

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tangent of 3/x

tangent of

\frac{3}{x}

y = - \frac{3}{a _{0}^{2}} x + \frac{6}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{3}{a _{0}})

Find the slope of

y = \frac{3}{x} : \frac{d y}{d x} = - \frac{3}{x ^{2}}

Compute the slope of

y = \frac{3}{x}

x = a_{0} : m = - \frac{3}{a _{0}^{2}}

Find the line with slope m=

- \frac{3}{a _{0}^{2}}

and passing through

(a_{0}, \frac{3}{a _{0}}) : y = - \frac{3}{a _{0}^{2}} x + \frac{6}{a _{0}}

y = - \frac{3}{a _{0}^{2}} x + \frac{6}{a _{0}}

\int 2 x (x^{2} + 5)^{5} d x

\frac{280}{s ^{2} + 14 s + 245}

\int m + n x d x

\frac{d}{d x} ((1 - 5 x)^{- 2})

y = e^{3 x} cos (π x), (0, 1)