What is taylor sin(x^3) ?

The answer to taylor sin(x^3) is x^3-1/6 x^9+\ldots

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taylor sin(x^3)

taylor

sin (x^{3})

x^{3} - \frac{1}{6} x^{9} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 60480}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= x^{3} - \frac{1}{6} x^{9} + \dots

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

\frac{\partial}{\partial x} (2 x^{3} y^{2})

x \to + 0 + lim (x^{x^{8}})

5 x y^{^{'}} - 2 y = - \frac{x ^{2}}{y ^{4}}