What is the tangent of 6/(sqrt(x)) ?

The tangent of 6/(sqrt(x)) is y=-3/(a_{0)^{3/2}}x+9/(sqrt(a_{0))}

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tangent of 6/(sqrt(x))

tangent of

\frac{6}{x}

y = - \frac{3}{a _{0}^{\frac{3}{2}}} x + \frac{9}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = \frac{6}{x} : \frac{d y}{d x} = - \frac{3}{x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{6}{x}

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

Find the line with slope m=

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

and passing through

(a_{0}, \frac{6}{a _{0}}) : y = - \frac{3}{a _{0}^{\frac{3}{2}}} x + \frac{9}{a _{0}}

y = - \frac{3}{a _{0}^{\frac{3}{2}}} x + \frac{9}{a _{0}}

\frac{1}{3 x ^{2} + 1}

n = 1 \sum \infty n^{- \frac{2}{3}}

2 (t - 3)^{2} + 9 (t - 3) + 11

y = 3 e^{4 x} + 6 e^{2 x}

\frac{d}{d x} (e^{7 x} + e^{- 7 x})

What is the tangent of 6/(sqrt(x)) ?
The tangent of 6/(sqrt(x)) is y=-3/(a_{0)^{3/2}}x+9/(sqrt(a_{0))}