What is taylor (x)^{(1/3)} ?

The answer to taylor (x)^{(1/3)} is 1+1/3 (x-1)-1/9 (x-1)^2+5/81 (x-1)^3-10/243 (x-1)^4+\ldots

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taylor (x)^{(1/3)}

taylor

(x)^{(\frac{1}{3})}

1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( x ^{\frac{1}{3}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{1}{3}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{1}{3}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{1}{3}}{1 !} (x - 1) + \frac{- \frac{2}{9}}{2 !} (x - 1)^{2} + \frac{\frac{10}{27}}{3 !} (x - 1)^{3} + \frac{- \frac{80}{81}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{1}{3} (x - 1) - \frac{1}{9} (x - 1)^{2} + \frac{5}{81} (x - 1)^{3} - \frac{10}{243} (x - 1)^{4} + \dots

\frac{\partial}{\partial x} (x^{7} y z^{2} + 3 yz)

\frac{d}{d x} (4 sin (5 x))

y = - x, y = \frac{1}{2} x - \frac{3}{2}, x = - 1, x = 3

\int_{0}^{1} x - x^{3} d x

y^{^{'}} (1 + x^{2}) + (1 + y^{2}) = 0

What is taylor (x)^{(1/3)} ?
The answer to taylor (x)^{(1/3)} is 1+1/3 (x-1)-1/9 (x-1)^2+5/81 (x-1)^3-10/243 (x-1)^4+\ldots