展开 f'(x)(1-3x^2)^3

解答

展开

f^{'} (x) (1 - 3 x^{2})^{3}

f' (x) - 9 x^{2} f' (x) + 27 x^{4} f' (x) - 27 x^{6} f' (x)

求解步骤

f^{'} (x) (1 - 3 x^{2})^{3}

(1 - 3 x^{2})^{3} = 1 - 9 x^{2} + 27 x^{4} - 27 x^{6}

= f^{^{'}} (x) (- 27 x^{6} + 27 x^{4} - 9 x^{2} + 1)

打开括号

= f^{^{'}} (x) 1 + f^{^{'}} (x) (- 9 x^{2}) + f^{^{'}} (x) 27 x^{4} + f^{^{'}} (x) (- 27 x^{6})

使用加减运算法则

+ (- a) = - a

= 1 f^{^{'}} (x) - 9 x^{2} f^{^{'}} (x) + 27 x^{4} f^{^{'}} (x) - 27 x^{6} f^{^{'}} (x)

乘以:

1 f^{'} (x) = f^{'} (x)

= f^{^{'}} (x) - 9 x^{2} f^{^{'}} (x) + 27 x^{4} f^{^{'}} (x) - 27 x^{6} f^{^{'}} (x)

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

s im pl i f y - 32 (1 - 37) + \frac{- 16 - 272 37}{27}

e x p an d (n + 2 i - n + i) n

e x p an d a (1 - e^{- b x})

e x p an d (x^{2} + 2 x - 5)^{7}