derivative of ln(sec(x+tan(x)))

解答

\frac{d}{d x} (ln (sec (x) + tan (x)))

sec (x)

求解步骤

\frac{d}{d x} (ln (sec (x) + tan (x)))

使用连锁律:

\frac{1}{sec ( x ) + tan ( x )} \frac{d}{d x} (sec (x) + tan (x))

= \frac{1}{sec ( x ) + tan ( x )} \frac{d}{d x} (sec (x) + tan (x))

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )})

化简

\frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : sec (x)

= sec (x)

\int 1200 e^{0.3 t} d t

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