What is taylor φ^3cos(φ^4) ?

The answer to taylor φ^3cos(φ^4) is φ^3+\ldots

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taylor φ^3cos(φ^4)

taylor

φ^{3} cos (φ^{4})

φ^{3} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= φ^{3} + \dots

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