What is the tangent of \sqrt[3]{x} ?

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

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tangent of \sqrt[3]{x}

tangent of

3 x

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

Find the slope of

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

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

(x - y) d x + d y = 0

x \to 0 lim (\frac{g ( x )}{f ( x )})

\int_{0}^{3} 4 d x

lo g_{8} (x e^{x})

\frac{d}{d x} (- tan (x) - 5 cot (x))

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