derivative 6x^5(x^4-8)

解答

导数

6 x^{5} (x^{4} - 8)

6 (9 x^{8} - 40 x^{4})

求解步骤

\frac{d}{d x} (6 x^{5} (x^{4} - 8))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (x^{5} (x^{4} - 8))

使用微分乘法定则:

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

f = x^{5}, g = x^{4} - 8

= 6 (\frac{d}{d x} (x^{5}) (x^{4} - 8) + \frac{d}{d x} (x^{4} - 8) x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (x^{4} - 8) = 4 x^{3}

= 6 (5 x^{4} (x^{4} - 8) + 4 x^{3} x^{5})

化简

6 (5 x^{4} (x^{4} - 8) + 4 x^{3} x^{5}) : 6 (9 x^{8} - 40 x^{4})

= 6 (9 x^{8} - 40 x^{4})

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