derivative (x^2+3)(x^2-3)x^2

解答

导数

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

6 x^{5} - 18 x

求解步骤

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

使用微分乘法定则:

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

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

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

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

\frac{d}{d x} ((x^{2} - 3) x^{2}) = 4 x^{3} - 6 x

= 2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3)

化简

2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3) : 6 x^{5} - 18 x

= 6 x^{5} - 18 x

\int sec^{2} (x) tan^{2} (x) d x

\frac{\partial}{\partial x} (- \frac{1}{x - y})

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\int \frac{1}{3} e^{- 3 x} d x