展开 (d^5)/d x^5(y=8x^4-16x^3-24x^2+32x+8)

解答

展开

\frac{d ^{5}}{d} x^{5} (y = 8 x^{4} - 16 x^{3} - 24 x^{2} + 32 x + 8)

d^{4} x^{5} y = 8 x^{4} - 16 d^{4} x^{8} - 24 d^{4} x^{7} + 32 d^{4} x^{6} + 8 d^{4} x^{5}

求解步骤

\frac{d ^{5}}{d} x^{5} (y = 8 x^{4} - 16 x^{3} - 24 x^{2} + 32 x + 8)

= \frac{d ^{5}}{d} x^{5} (8 = x^{4} y - 16 x^{3} - 24 x^{2} + 32 x + 8)

打开括号

\frac{d ^{5}}{d} x^{5} y = 8 x^{4} + \frac{d ^{5}}{d} x^{5} (- 16 x^{3}) + \frac{d ^{5}}{d} x^{5} (- 24 x^{2}) + \frac{d ^{5}}{d} x^{5} \cdot 32 x + \frac{d ^{5}}{d} x^{5} \cdot 8

使用加减运算法则

+ (- a) = - a

\frac{d ^{5}}{d} x^{5} y = 8 x^{4} - 16 \cdot \frac{d ^{5}}{d} x^{5} x^{3} - 24 \cdot \frac{d ^{5}}{d} x^{5} x^{2} + 32 \cdot \frac{d ^{5}}{d} x^{5} x + 8 \cdot \frac{d ^{5}}{d} x^{5}

化简

\frac{d ^{5}}{d} x^{5} y = 8 x^{4} - 16 \cdot \frac{d ^{5}}{d} x^{5} x^{3} - 24 \cdot \frac{d ^{5}}{d} x^{5} x^{2} + 32 \cdot \frac{d ^{5}}{d} x^{5} x + 8 \cdot \frac{d ^{5}}{d} x^{5} : d^{4} x^{5} y = 8 x^{4} - 16 d^{4} x^{8} - 24 d^{4} x^{7} + 32 d^{4} x^{6} + 8 d^{4} x^{5}

d^{4} x^{5} y = 8 x^{4} - 16 d^{4} x^{8} - 24 d^{4} x^{7} + 32 d^{4} x^{6} + 8 d^{4} x^{5}

e x p an d \frac{( 1 - cos ( 2 x - 2 ) )}{( x - 1 ) ^{2}}

e x p an d x^{2} (x + 1) d x + y^{2} (x - 1)

e x p an d \frac{A ( 2 - x ^{2} - y ^{2} )}{2}

e x p an d (\frac{2}{3}, \frac{10}{3}) y (- \frac{8}{3}, - \frac{10}{3})

e x p an d \frac{( n + 1 ) n ( n - 1 )}{6}