What is taylor cos(x^2)sin(x) ?

The answer to taylor cos(x^2)sin(x) is x-1/6 x^3-59/120 x^5+\ldots

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taylor cos(x^2)sin(x)

taylor

cos (x^{2}) sin (x)

x - \frac{1}{6} x^{3} - \frac{59}{120} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{1}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 1}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 59}{5 !} x^{5} + \dots

Refine

= x - \frac{1}{6} x^{3} - \frac{59}{120} x^{5} + \dots

\frac{x - 5}{9 x ^{2} e ^{x}}

\frac{\partial}{\partial x} (2 x + y)

y^{^{'''}} + 3 y^{^{''}} + y^{^{'}} - 5 y = 0

\int 7 x^{6} d x

10 x e^{x}

What is taylor cos(x^2)sin(x) ?
The answer to taylor cos(x^2)sin(x) is x-1/6 x^3-59/120 x^5+\ldots