泰勒 11sin(-x)

解答

泰勒

11 sin (- x)

- 11 x + \frac{11}{6} x^{3} - \frac{11}{120} x^{5} + \frac{11}{5040} x^{7} - \frac{11}{362880} x^{9} + \dots

求解步骤

应用泰勒公式

= 0 + \frac{\frac{d}{d x} ( 11 sin ( - x ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( 11 sin ( - x ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 11 sin ( - x ) ) ( 0 )}{3 !} x^{3} + \dots

求导数

= 0 + \frac{- 11}{1 !} x + \frac{0}{2 !} x^{2} + \frac{11}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{- 11}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{11}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 11}{9 !} x^{9} + \dots

整理后得

= - 11 x + \frac{11}{6} x^{3} - \frac{11}{120} x^{5} + \frac{11}{5040} x^{7} - \frac{11}{362880} x^{9} + \dots

\frac{d}{d x} (\frac{2 x + 5}{3 x - 2})

\frac{d}{d x} (3 x + \frac{2}{x})

\frac{\partial}{\partial x} (sin (- 3 x) cos (4 y))

\frac{d}{d x} (x^{3} - 6 x^{2} + 11 x - 6)

a re a y = 7 3 x, 0 \leq x \leq 27