derivative y=x^3(9-x^2)

解答

导数

y = x^{3} (9 - x^{2})

27 x^{2} - 5 x^{4}

求解步骤

\frac{d}{d x} (x^{3} (9 - x^{2}))

使用微分乘法定则:

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

f = x^{3}, g = 9 - x^{2}

= \frac{d}{d x} (x^{3}) (9 - x^{2}) + \frac{d}{d x} (9 - x^{2}) x^{3}

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

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 3 x^{2} (9 - x^{2}) + (- 2 x) x^{3}

化简

3 x^{2} (9 - x^{2}) + (- 2 x) x^{3} : 27 x^{2} - 5 x^{4}

= 27 x^{2} - 5 x^{4}

d er i v a t i v e 2 x^{7} + 3 x + 11

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