What is taylor 2sin(x^2) ?

The answer to taylor 2sin(x^2) is 2x^2-1/3 x^6+1/60 x^{10}+\ldots

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taylor 2sin(x^2)

taylor

2 sin (x^{2})

2 x^{2} - \frac{1}{3} x^{6} + \frac{1}{60} x^{10} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{- 240}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{60480}{10 !} x^{10} + \dots

Refine

= 2 x^{2} - \frac{1}{3} x^{6} + \frac{1}{60} x^{10} + \dots

\int 2 sec^{2} (x) tan (x) d x

t^{3} e^{- 2 t}

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

(e^{- 5 x})^{^{'}}

\int \frac{x + 4}{x} d x

What is taylor 2sin(x^2) ?
The answer to taylor 2sin(x^2) is 2x^2-1/3 x^6+1/60 x^{10}+\ldots