What is taylor x^4cos(x^3) ?

The answer to taylor x^4cos(x^3) is x^4-1/2 x^{10}+\ldots

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taylor x^4cos(x^3)

taylor

x^{4} cos (x^{3})

x^{4} - \frac{1}{2} x^{10} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( x ^{4} cos ( x ^{3} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{4} cos ( x ^{3} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{4} cos ( x ^{3} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{- 1814400}{10 !} x^{10} + \dots

Refine

= x^{4} - \frac{1}{2} x^{10} + \dots

\frac{\partial}{\partial x} (4 cos (x^{2} + y^{2}))

e^{t} cos (6 t)

5 - x^{2}

f (x) = ln (x^{2} + 3)

y = (x + 1) (x + 2)

What is taylor x^4cos(x^3) ?
The answer to taylor x^4cos(x^3) is x^4-1/2 x^{10}+\ldots