derivative f(x)= 6/(ln(x^2+4))

解答

导数

f (x) = \frac{6}{ln ( x ^{2} + 4 )}

- \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

求解步骤

\frac{d}{d x} (\frac{6}{ln ( x ^{2} + 4 )})

将常数提出:

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

= 6 \frac{d}{d x} (\frac{1}{ln ( x ^{2} + 4 )})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 6 \frac{d}{d x} (ln^{- 1} (x^{2} + 4))

使用连锁律:

- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

= - \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \frac{d}{d x} (ln (x^{2} + 4))

\frac{d}{d x} (ln (x^{2} + 4)) = \frac{2 x}{x ^{2} + 4}

= 6 (- \frac{1}{( ln ( x ^{2} + 4 ) ) ^{2}} \cdot \frac{2 x}{x ^{2} + 4})

化简

6 (- \frac{1}{ln ^{2} ( x ^{2} + 4 )} \cdot \frac{2 x}{x ^{2} + 4}) : - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

= - \frac{12 x}{ln ^{2} ( x ^{2} + 4 ) ( x ^{2} + 4 )}

\int \frac{sin ( 44 x )}{1 + cos ^{2} ( 44 x )} d x

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a re a f (x) = x^{2}, [0, 3]

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