展开 f'(x)(x^2-2x)^5

解答

展开

f^{'} (x) (x^{2} - 2 x)^{5}

x^{10} f' (x) - 10 x^{9} f' (x) + 40 x^{8} f' (x) - 80 x^{7} f' (x) + 80 x^{6} f' (x) - 32 x^{5} f' (x)

求解步骤

f^{'} (x) (x^{2} - 2 x)^{5}

(x^{2} - 2 x)^{5} = x^{10} - 10 x^{9} + 40 x^{8} - 80 x^{7} + 80 x^{6} - 32 x^{5}

= f^{^{'}} (x) (x^{10} - 10 x^{9} + 40 x^{8} - 80 x^{7} + 80 x^{6} - 32 x^{5})

打开括号

= f^{^{'}} (x) x^{10} + f^{^{'}} (x) (- 10 x^{9}) + f^{^{'}} (x) 40 x^{8} + f^{^{'}} (x) (- 80 x^{7}) + f^{^{'}} (x) 80 x^{6} + f^{^{'}} (x) (- 32 x^{5})

使用加减运算法则

+ (- a) = - a

= x^{10} f^{^{'}} (x) - 10 x^{9} f^{^{'}} (x) + 40 x^{8} f^{^{'}} (x) - 80 x^{7} f^{^{'}} (x) + 80 x^{6} f^{^{'}} (x) - 32 x^{5} f^{^{'}} (x)

e x p an d \frac{d x}{d} (x = 200 - 2 y)

e x p an d 1125 - 200 \cdot (75 - x)^{2} d x

s im pl i f y \frac{18.6}{( 1 - 3 x ) ^{2}}

e x p an d A! B +! A B (C + C)

e x p an d - \frac{1}{3} x + 1