What is maclaurin e^{sin(2x)} ?

The answer to maclaurin e^{sin(2x)} is 1+2x+2x^2-2x^4-32/15 x^5+\ldots

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maclaurin e^{sin(2x)}

maclaurin

e^{s i n (2 x)}

1 + 2 x + 2 x^{2} - 2 x^{4} - \frac{32}{15} x^{5} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( e ^{s i n (2 x)} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{s i n (2 x)} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{s i n (2 x)} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{- 48}{4 !} x^{4} + \frac{- 256}{5 !} x^{5} + \dots

Refine

= 1 + 2 x + 2 x^{2} - 2 x^{4} - \frac{32}{15} x^{5} + \dots

\int - 2 cos (x) + 3 x^{2} - 5 x + 4 d x

\int 3 x + \frac{1}{3 x} d x

y^{^{''}} - 6 y^{^{'}} + 7 y = 0, y (0) = 0, y^{^{'}} (0) = 7

\frac{d}{d x} (x e^{\frac{y}{z}})

7 x - 6 x

What is maclaurin e^{sin(2x)} ?
The answer to maclaurin e^{sin(2x)} is 1+2x+2x^2-2x^4-32/15 x^5+\ldots