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

解答

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

- e^{x^{2} - s e c (x)} tan (e^{x^{2} - s e c (x)}) (2 x - sec (x) tan (x))

求解步骤

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

使用连锁律:

\frac{1}{cos ( e ^{x^{2} - s e c (x)} )} \frac{d}{d x} (cos (e^{x^{2} - s e c (x)}))

= \frac{1}{cos ( e ^{x^{2} - s e c (x)} )} \frac{d}{d x} (cos (e^{x^{2} - s e c (x)}))

\frac{d}{d x} (cos (e^{x^{2} - s e c (x)})) = - sin (e^{x^{2} - s e c (x)}) e^{x^{2} - s e c (x)} (2 x - sec (x) tan (x))

= \frac{1}{cos ( e ^{x^{2} - s e c (x)} )} (- sin (e^{x^{2} - s e c (x)}) e^{x^{2} - s e c (x)} (2 x - sec (x) tan (x)))

化简

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

= - e^{x^{2} - s e c (x)} tan (e^{x^{2} - s e c (x)}) (2 x - sec (x) tan (x))

\int 4 ln (3 x) d x

\int \frac{9 e ^{- \frac{1}{x}}}{x ^{2}} d x

t an g e n t f (x) = x^{2} + 1, at x = 2

t an g e n t x^{4} - 4 x^{2} + 10, at x = 1

y^{^{'}} + x y = 0