泰勒 X^{9/6},7

解答

泰勒

X^{\frac{9}{6}}, 7

7 \cdot 7^{\frac{1}{2}} + \frac{3 \cdot 7 ^{\frac{1}{2}}}{2} (X - 7) + \frac{3}{8 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{2} - \frac{1}{112 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{3} + \frac{3}{6272 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{4} + \dots

求解步骤

应用泰勒公式

= 7 \cdot 7^{\frac{1}{2}} + \frac{\frac{d}{d X} ( X ^{\frac{9}{6}} ) ( 7 )}{1 !} (X - 7) + \frac{\frac{d ^{2}}{d X ^{2}} ( X ^{\frac{9}{6}} ) ( 7 )}{2 !} (X - 7)^{2} + \frac{\frac{d ^{3}}{d X ^{3}} ( X ^{\frac{9}{6}} ) ( 7 )}{3 !} (X - 7)^{3} + \dots

求导数

= 7 \cdot 7^{\frac{1}{2}} + \frac{\frac{3 \cdot 7 ^{\frac{1}{2}}}{2}}{1 !} (X - 7) + \frac{\frac{3}{4 \cdot 7 ^{\frac{1}{2}}}}{2 !} (X - 7)^{2} + \frac{- \frac{3}{56 \cdot 7 ^{\frac{1}{2}}}}{3 !} (X - 7)^{3} + \frac{\frac{9}{784 \cdot 7 ^{\frac{1}{2}}}}{4 !} (X - 7)^{4} + \dots

整理后得

= 7 \cdot 7^{\frac{1}{2}} + \frac{3 \cdot 7 ^{\frac{1}{2}}}{2} (X - 7) + \frac{3}{8 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{2} - \frac{1}{112 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{3} + \frac{3}{6272 \cdot 7 ^{\frac{1}{2}}} (X - 7)^{4} + \dots

\frac{d}{d x} (tan (3^{x}))

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

d er i v a t i v e \frac{x}{x + 9}

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

\int_{0}^{1} \frac{x}{( x + 1 ) ( x ^{2} + 1 )} d x