展开 6x(x^2-5)^2

解答

展开

6 x (x^{2} - 5)^{2}

6 x^{5} - 60 x^{3} + 150 x

求解步骤

6 x (x^{2} - 5)^{2}

展开

(x^{2} - 5)^{2} : x^{4} - 10 x^{2} + 25

= 6 x (x^{4} - 10 x^{2} + 25)

使用分配律:

m (a + b + c) = ma + mb + m c

6 x (x^{4} - 10 x^{2} + 25) = 6 x x^{4} + 6 x (- 10 x^{2}) + 6 x \cdot 25

= 6 x x^{4} + 6 x (- 10 x^{2}) + 6 x \cdot 25

化简

6 x x^{4} + 6 x (- 10 x^{2}) + 6 x \cdot 25 : 6 x^{5} - 60 x^{3} + 150 x

= 6 x^{5} - 60 x^{3} + 150 x

\frac{d}{d x} (\frac{9 x}{x + 4})

\frac{d y}{d x} = 4 y^{2}

s l o p e f (x) = 3 x - x^{2}

d er i v a t i v e f (x) = 9 (5^{x})

d er i v a t i v e f (x) = c x^{- 6}