What is the tangent of y=x^{1/3} ?

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

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tangent of y=x^{1/3}

tangent of

y = x^{\frac{1}{3}}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{\frac{1}{3}})

Find the slope of

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

Compute the slope of

y = x^{\frac{1}{3}}

x = a_{0} : m = \frac{1}{3 a _{0}^{\frac{2}{3}}}

Find the line with slope m=

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

and passing through

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

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

t \to 1 lim (ln (t - 1))

\frac{d}{d x} ((\frac{x ^{2}}{4} + 5 x - \frac{1}{x})^{3})

\frac{( 3 s + 5 )}{2 s ^{2} + 6 s + 4}

\int x^{- 2} (x^{6} - 2 x^{3} + 1) d x

\frac{d}{d x} (3 x^{- 2} - \frac{1}{x})

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