derivative f(x)=(x^2-7)(x^2+6)

解答

导数

f (x) = (x^{2} - 7) (x^{2} + 6)

4 x^{3} - 2 x

求解步骤

\frac{d}{d x} ((x^{2} - 7) (x^{2} + 6))

使用微分乘法定则:

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

f = x^{2} - 7, g = x^{2} + 6

= \frac{d}{d x} (x^{2} - 7) (x^{2} + 6) + \frac{d}{d x} (x^{2} + 6) (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = 2 x

\frac{d}{d x} (x^{2} + 6) = 2 x

= 2 x (x^{2} + 6) + 2 x (x^{2} - 7)

化简

2 x (x^{2} + 6) + 2 x (x^{2} - 7) : 4 x^{3} - 2 x

= 4 x^{3} - 2 x

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