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

解答

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

- 20 x (3 - x^{2})^{4}

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用连锁律:

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

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

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

= 2 \cdot 5 (3 - x^{2})^{4} (- 2 x)

化简

= - 20 x (3 - x^{2})^{4}

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