derivative of x^4(x-3^3)

解答

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

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

求解步骤

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

使用微分乘法定则:

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

f = x^{4}, g = (x - 3)^{3}

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

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

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

= 4 x^{3} (x - 3)^{3} + 3 (x - 3)^{2} x^{4}

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