What is the tangent of x^{2/3} ?

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

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tangent of x^{2/3}

tangent of

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

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{\frac{2}{3}})

Find the slope of

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

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

Find the line with slope m=

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

and passing through

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

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

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