derivative (3x+1)^4(5-2x)^3

解答

导数

(3 x + 1)^{4} (5 - 2 x)^{3}

12 (3 x + 1)^{3} (5 - 2 x)^{3} - 6 (5 - 2 x)^{2} (3 x + 1)^{4}

求解步骤

\frac{d}{d x} ((3 x + 1)^{4} (5 - 2 x)^{3})

使用微分乘法定则:

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

f = (3 x + 1)^{4}, g = (5 - 2 x)^{3}

= \frac{d}{d x} ((3 x + 1)^{4}) (5 - 2 x)^{3} + \frac{d}{d x} ((5 - 2 x)^{3}) (3 x + 1)^{4}

\frac{d}{d x} ((3 x + 1)^{4}) = 12 (3 x + 1)^{3}

\frac{d}{d x} ((5 - 2 x)^{3}) = - 6 (5 - 2 x)^{2}

= 12 (3 x + 1)^{3} (5 - 2 x)^{3} + (- 6 (5 - 2 x)^{2}) (3 x + 1)^{4}

化简

= 12 (3 x + 1)^{3} (5 - 2 x)^{3} - 6 (5 - 2 x)^{2} (3 x + 1)^{4}

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