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

解答

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

10 (2 x + 1)^{4} (x^{3} - x + 1)^{4} + 4 (x^{3} - x + 1)^{3} (3 x^{2} - 1) (2 x + 1)^{5}

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

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

= 10 (2 x + 1)^{4} (x^{3} - x + 1)^{4} + 4 (x^{3} - x + 1)^{3} (3 x^{2} - 1) (2 x + 1)^{5}

\int 2 - 2 cos (x) d x

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