What is maclaurin x*cos(x) ?

The answer to maclaurin x*cos(x) is x-1/2 x^3+1/24 x^5-1/720 x^7+1/40320 x^9+\ldots

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maclaurin x*cos(x)

maclaurin

x \cdot cos (x)

x - \frac{1}{2} x^{3} + \frac{1}{24} x^{5} - \frac{1}{720} x^{7} + \frac{1}{40320} x^{9} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Refine

= x - \frac{1}{2} x^{3} + \frac{1}{24} x^{5} - \frac{1}{720} x^{7} + \frac{1}{40320} x^{9} + \dots

\frac{\partial}{\partial x} (9 y e^{7 x})

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\int \frac{e ^{x}}{( e ^{x} - 5 ) ( e ^{2 x} + 1 )} d x

What is maclaurin x*cos(x) ?
The answer to maclaurin x*cos(x) is x-1/2 x^3+1/24 x^5-1/720 x^7+1/40320 x^9+\ldots