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

解答

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

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

求解步骤

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

使用微分乘法定则:

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

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

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

\frac{d}{d x} ((3 x^{2} + 5)^{3}) = 18 x (3 x^{2} + 5)^{2}

\frac{d}{d x} ((3 x - 1)^{2}) = 6 (3 x - 1)

= 18 x (3 x^{2} + 5)^{2} (3 x - 1)^{2} + 6 (3 x - 1) (3 x^{2} + 5)^{3}

\int (1 + x^{2})^{- 1} d x

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d er i v a t i v e - csc (x) - sin (x)