展开 f''(x)(x-1)(x-3)^2

解答

展开

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

x^{3} f'' (x) - 7 x^{2} f'' (x) + 15 x f'' (x) - 9 f'' (x)

求解步骤

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

使用分配律:

a (b - c) = ab - a c

a = f^{''} (x) (x - 3)^{2}, b = x, c = 1

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

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

化简

x f^{''} (x) (x - 3)^{2} - 1 f^{''} (x) (x - 3)^{2} : x^{3} f^{''} (x) - 7 x^{2} f^{''} (x) + 15 x f^{''} (x) - 9 f^{''} (x)

= x^{3} f^{''} (x) - 7 x^{2} f^{''} (x) + 15 x f^{''} (x) - 9 f^{''} (x)

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