泰勒 x^{9/6},5

解答

泰勒

x^{\frac{9}{6}}, 5

5 \cdot 5^{\frac{1}{2}} + \frac{3 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{3}{8 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{2} - \frac{1}{80 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{3} + \frac{3}{3200 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{4} + \dots

求解步骤

应用泰勒公式

= 5 \cdot 5^{\frac{1}{2}} + \frac{\frac{d}{d x} ( x ^{\frac{9}{6}} ) ( 5 )}{1 !} (x - 5) + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{\frac{9}{6}} ) ( 5 )}{2 !} (x - 5)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{\frac{9}{6}} ) ( 5 )}{3 !} (x - 5)^{3} + \dots

求导数

= 5 \cdot 5^{\frac{1}{2}} + \frac{\frac{3 \cdot 5 ^{\frac{1}{2}}}{2}}{1 !} (x - 5) + \frac{\frac{3}{4 \cdot 5 ^{\frac{1}{2}}}}{2 !} (x - 5)^{2} + \frac{- \frac{3}{40 \cdot 5 ^{\frac{1}{2}}}}{3 !} (x - 5)^{3} + \frac{\frac{9}{400 \cdot 5 ^{\frac{1}{2}}}}{4 !} (x - 5)^{4} + \dots

整理后得

= 5 \cdot 5^{\frac{1}{2}} + \frac{3 \cdot 5 ^{\frac{1}{2}}}{2} (x - 5) + \frac{3}{8 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{2} - \frac{1}{80 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{3} + \frac{3}{3200 \cdot 5 ^{\frac{1}{2}}} (x - 5)^{4} + \dots

\frac{d}{d x} (10500 x + \frac{1}{5} x^{5} + 1900)

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

l a pl a ce t r an s f or m t e^{2 t}

d er i v a t i v e sin^{2} (p i x)

\frac{d}{d x} (ln (x + 4))