derivative y=ln((cos(x))/(cos(x)-1))

解答

导数

y = ln (\frac{cos ( x )}{cos ( x ) - 1})

\frac{tan ( x )}{cos ( x ) - 1}

求解步骤

\frac{d}{d x} (ln (\frac{cos ( x )}{cos ( x ) - 1}))

使用连锁律:

\frac{1}{\frac{c o s ( x )}{c o s ( x ) - 1}} \frac{d}{d x} (\frac{cos ( x )}{cos ( x ) - 1})

= \frac{1}{\frac{c o s ( x )}{c o s ( x ) - 1}} \frac{d}{d x} (\frac{cos ( x )}{cos ( x ) - 1})

\frac{d}{d x} (\frac{cos ( x )}{cos ( x ) - 1}) = \frac{sin ( x )}{( cos ( x ) - 1 ) ^{2}}

= \frac{1}{\frac{c o s ( x )}{c o s ( x ) - 1}} \cdot \frac{sin ( x )}{( cos ( x ) - 1 ) ^{2}}

化简

\frac{1}{\frac{c o s ( x )}{c o s ( x ) - 1}} \cdot \frac{sin ( x )}{( cos ( x ) - 1 ) ^{2}} : \frac{tan ( x )}{cos ( x ) - 1}

= \frac{tan ( x )}{cos ( x ) - 1}

\int 3 x^{9} e^{- x^{5}} d x

\int \frac{x ^{2}}{x - 8} d x

\int_{- \infty}^{0} \frac{1}{x ^{2}} d x

e^{- y} (1 + \frac{d y}{d x}) = 1

\int (t - 1) e^{- s t} d t