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

解答

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

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

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} ((x^{2} - 4)^{5}) = 10 x (x^{2} - 4)^{4}

\frac{d}{d x} ((3 x + 5)^{4}) = 12 (3 x + 5)^{3}

= 10 x (x^{2} - 4)^{4} (3 x + 5)^{4} + 12 (3 x + 5)^{3} (x^{2} - 4)^{5}

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