What is taylor (x+x*cos(x)-2*sin(x))/(x^3) ?

The answer to taylor (x+x*cos(x)-2*sin(x))/(x^3) is

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taylor (x+xcos(x)-2sin(x))/(x^3)

taylor

\frac{x + x \cdot cos ( x ) - 2 \cdot sin ( x )}{x ^{3}}

1 + cos (1) - 2 sin (1) + (5 sin (1) - 4 cos (1) - 2) (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{6} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{24} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + cos (1) - 2 sin (1) + \frac{\frac{d}{d x} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{x + x c o s ( x ) - 2 s i n ( x )}{x ^{3}} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 1 + cos (1) - 2 sin (1) + \frac{5 sin ( 1 ) - 4 cos ( 1 ) - 2}{1 !} (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2 !} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{3 !} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + cos (1) - 2 sin (1) + (5 sin (1) - 4 cos (1) - 2) (x - 1) + \frac{17 cos ( 1 ) - 18 sin ( 1 ) + 6}{2} (x - 1)^{2} + \frac{85 sin ( 1 ) - 88 cos ( 1 ) - 24}{6} (x - 1)^{3} + \frac{541 cos ( 1 ) - 490 sin ( 1 ) + 120}{24} (x - 1)^{4} + \dots

\frac{d}{d x} (2 x^{4} + 2 y^{4} + z^{4} - 2 x^{2} y^{2} z)

\int - \frac{3}{y} d y

\frac{\partial}{\partial x} (\frac{x - y}{x + y} - y^{3})

\frac{3}{( s + 1 ) ^{2} + 9}

\frac{d}{d x} (tan (13 x))

What is taylor (x+x*cos(x)-2*sin(x))/(x^3) ?
The answer to taylor (x+x*cos(x)-2*sin(x))/(x^3) is