derivative 8sqrt(3x^2+9)

解答

导数

8 3 x^{2} + 9

\frac{24 x}{3 x ^{2} + 9}

求解步骤

\frac{d}{d x} (8 3 x^{2} + 9)

将常数提出:

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

= 8 \frac{d}{d x} (3 x^{2} + 9)

使用连锁律:

\frac{1}{2 3 x ^{2} + 9} \frac{d}{d x} (3 x^{2} + 9)

= \frac{1}{2 3 x ^{2} + 9} \frac{d}{d x} (3 x^{2} + 9)

\frac{d}{d x} (3 x^{2} + 9) = 6 x

= 8 \cdot \frac{1}{2 3 x ^{2} + 9} \cdot 6 x

化简

8 \cdot \frac{1}{2 3 x ^{2} + 9} \cdot 6 x : \frac{24 x}{3 x ^{2} + 9}

= \frac{24 x}{3 x ^{2} + 9}

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