derivative ln(csc(x)-cot(x))

解答

导数

ln (csc (x) - cot (x))

\frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

求解步骤

\frac{d}{d x} (ln (csc (x) - cot (x)))

使用连锁律:

\frac{1}{csc ( x ) - cot ( x )} \frac{d}{d x} (csc (x) - cot (x))

= \frac{1}{csc ( x ) - cot ( x )} \frac{d}{d x} (csc (x) - cot (x))

\frac{d}{d x} (csc (x) - cot (x)) = \frac{1}{1 + cos ( x )}

= \frac{1}{csc ( x ) - cot ( x )} \cdot \frac{1}{1 + cos ( x )}

化简

\frac{1}{csc ( x ) - cot ( x )} \cdot \frac{1}{1 + cos ( x )} : \frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

= \frac{1}{( csc ( x ) - cot ( x ) ) ( 1 + cos ( x ) )}

\int \frac{x + 5}{x ^{2} - 16} d x

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