derivative of (x+1^2(x-5))

解答

\frac{d}{d x} ((x + 1)^{2} (x - 5))

3 x^{2} - 6 x - 9

求解步骤

\frac{d}{d x} ((x + 1)^{2} (x - 5))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x + 1)^{2}, g = x - 5

= \frac{d}{d x} ((x + 1)^{2}) (x - 5) + \frac{d}{d x} (x - 5) (x + 1)^{2}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

\frac{d}{d x} (x - 5) = 1

= 2 (x + 1) (x - 5) + 1 \cdot (x + 1)^{2}

化简

2 (x + 1) (x - 5) + 1 \cdot (x + 1)^{2} : 3 x^{2} - 6 x - 9

= 3 x^{2} - 6 x - 9

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