What is maclaurin 6sin(2x) ?

The answer to maclaurin 6sin(2x) is 12x-8x^3+8/5 x^5-16/105 x^7+8/945 x^9+\ldots

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maclaurin 6sin(2x)

maclaurin

6 sin (2 x)

12 x - 8 x^{3} + \frac{8}{5} x^{5} - \frac{16}{105} x^{7} + \frac{8}{945} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( 6 sin ( 2 x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 6 sin ( 2 x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 6 sin ( 2 x ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{12}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 48}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{192}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{- 768}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{3072}{9 !} x^{9} + \dots

Refine

= 12 x - 8 x^{3} + \frac{8}{5} x^{5} - \frac{16}{105} x^{7} + \frac{8}{945} x^{9} + \dots

\int x^{5} sin (2 x) d x

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

t \frac{d y}{d t} + 30 y = \frac{1}{t}

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

(8.4) (5.2)

What is maclaurin 6sin(2x) ?
The answer to maclaurin 6sin(2x) is 12x-8x^3+8/5 x^5-16/105 x^7+8/945 x^9+\ldots