derivative of cos(ln(sec(e^{-2x})))

解答

\frac{d}{d x} (cos (ln (sec (e^{- 2 x}))))

2 e^{- 2 x} sin (ln (sec (e^{- 2 x}))) tan (e^{- 2 x})

求解步骤

\frac{d}{d x} (cos (ln (sec (e^{- 2 x}))))

使用连锁律:

- sin (ln (sec (e^{- 2 x}))) \frac{d}{d x} (ln (sec (e^{- 2 x})))

= - sin (ln (sec (e^{- 2 x}))) \frac{d}{d x} (ln (sec (e^{- 2 x})))

\frac{d}{d x} (ln (sec (e^{- 2 x}))) = - 2 e^{- 2 x} tan (e^{- 2 x})

= - sin (ln (sec (e^{- 2 x}))) (- 2 e^{- 2 x} tan (e^{- 2 x}))

化简

= 2 e^{- 2 x} sin (ln (sec (e^{- 2 x}))) tan (e^{- 2 x})

d er i v a t i v e f (x) = (5 x - 5) (x + 3)

\frac{d}{d x} (\frac{x}{1 + x ^{3}})

x \to 0 lim ((1 - 4 x)^{\frac{8}{x}})

x \to 4 lim (\frac{1}{2 + x})

d er i v a t i v e y = sin^{2} (e^{s i n^{2} (t)})