What is taylor sin(x)*e^x ?

The answer to taylor sin(x)*e^x is x+x^2+1/3 x^3-1/30 x^5-1/90 x^6+\ldots

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taylor sin(x)*e^x

taylor

sin (x) \cdot e^{x}

x + x^{2} + \frac{1}{3} x^{3} - \frac{1}{30} x^{5} - \frac{1}{90} x^{6} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= x + x^{2} + \frac{1}{3} x^{3} - \frac{1}{30} x^{5} - \frac{1}{90} x^{6} + \dots

\frac{\partial}{\partial x} (- 3 x y (- 12 - x - y))

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

\int_{- 1}^{4} (3 x^{2} + 8 x - 5) d x

\int 2 x^{4} + e^{2 x} + sin (3 x) d x

f (x) = \frac{4}{1 + x ^{2}}

What is taylor sin(x)*e^x ?
The answer to taylor sin(x)*e^x is x+x^2+1/3 x^3-1/30 x^5-1/90 x^6+\ldots