What is taylor cos(x^3) ?

The answer to taylor cos(x^3) is 1-1/2 x^6+\ldots

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taylor cos(x^3)

taylor

cos (x^{3})

1 - \frac{1}{2} x^{6} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 360}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - \frac{1}{2} x^{6} + \dots

\int_{1}^{\infty} 5 e^{- 5 x} d x

\int e^{- x^{2}} d x

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

\frac{d}{d x} (x^{4} + 4 x^{3} - 2 x^{2} - 12 x)