derivative f(x)=sqrt(12x+\sqrt{x)}

解答

导数

f (x) = 12 x + x

\frac{24 x + 1}{4 x 12 x + x}

求解步骤

\frac{d}{d x} (12 x + x)

使用连锁律:

\frac{1}{2 12 x + x} \frac{d}{d x} (12 x + x)

= \frac{1}{2 12 x + x} \frac{d}{d x} (12 x + x)

\frac{d}{d x} (12 x + x) = 12 + \frac{1}{2 x}

= \frac{1}{2 12 x + x} (12 + \frac{1}{2 x})

化简

\frac{1}{2 12 x + x} (12 + \frac{1}{2 x}) : \frac{24 x + 1}{4 x 12 x + x}

= \frac{24 x + 1}{4 x 12 x + x}

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