What is taylor xsin(x^3) ?

The answer to taylor xsin(x^3) is x^4-1/6 x^{10}+\ldots

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taylor xsin(x^3)

taylor

x sin (x^{3})

x^{4} - \frac{1}{6} x^{10} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x sin ( x ^{3} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x sin ( x ^{3} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x sin ( x ^{3} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{- 604800}{10 !} x^{10} + \dots

Refine

= x^{4} - \frac{1}{6} x^{10} + \dots

x^{- \frac{2}{4}} + x^{\frac{2}{4}}

\int_{0}^{\infty} 3 e^{- 3 x} d x

\int_{0}^{1} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

\frac{d}{d x} ((8 x)^{\frac{1}{3}})

What is taylor xsin(x^3) ?
The answer to taylor xsin(x^3) is x^4-1/6 x^{10}+\ldots