derivative log_{10}(x^2+1)

解答

导数

lo g_{10} (x^{2} + 1)

\frac{2 x}{ln ( 10 ) ( x ^{2} + 1 )}

求解步骤

\frac{d}{d x} (lo g_{10} (x^{2} + 1))

使用对数计算法则:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( x ^{2} + 1 )}{ln ( 10 )})

将常数提出:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x^{2} + 1))

使用连锁律:

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

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

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 1} \cdot 2 x

化简

\frac{1}{ln ( 10 )} \cdot \frac{1}{x ^{2} + 1} \cdot 2 x : \frac{2 x}{ln ( 10 ) ( x ^{2} + 1 )}

= \frac{2 x}{ln ( 10 ) ( x ^{2} + 1 )}

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