麦克劳林 4/(1+x)

解答

麦克劳林

\frac{4}{1 + x}

4 - 4 x + 4 x^{2} - 4 x^{3} + 4 x^{4} + \dots

求解步骤

应用麦克劳林公式

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

求导数

= 4 + \frac{- 4}{1 !} x + \frac{8}{2 !} x^{2} + \frac{- 24}{3 !} x^{3} + \frac{96}{4 !} x^{4} + \dots

整理后得

= 4 - 4 x + 4 x^{2} - 4 x^{3} + 4 x^{4} + \dots

\frac{d}{d x} (sin (2 x^{4}))

\frac{d}{d x} (\frac{1}{- sin ( x )})

\frac{d}{d x} (4 2 x^{2} - 4 x + 7)

\int ((1 - (\frac{x ^{2}}{9})))^{\frac{1}{2}} d x

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