What is the tangent of 1/(sqrt(3x)) ?

The tangent of 1/(sqrt(3x)) is y=-1/(2sqrt(3)a_{0)^{3/2}}x+(sqrt(3))/(2sqrt(a_{0))}

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tangent of 1/(sqrt(3x))

tangent of

\frac{1}{3 x}

y = - \frac{1}{2 3 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{3 a _{0}})

Find the slope of

y = \frac{1}{3 x} : \frac{d y}{d x} = - \frac{1}{2 3 x ^{\frac{3}{2}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{1}{2 3 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{1}{2 3 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{1}{3 a _{0}}) : y = - \frac{1}{2 3 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 a _{0}}

y = - \frac{1}{2 3 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 a _{0}}

What is the tangent of 1/(sqrt(3x)) ?
The tangent of 1/(sqrt(3x)) is y=-1/(2sqrt(3)a_{0)^{3/2}}x+(sqrt(3))/(2sqrt(a_{0))}