derivative of (sech(2x)^{sin(3x)})

解

\frac{d}{d x} ((sech (2 x))^{s i n (3 x)})

sech^{s i n (3 x)} (2 x) (3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x))

解答ステップ

\frac{d}{d x} ((sech (2 x))^{s i n (3 x)})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

(sech (2 x))^{s i n (3 x)} = e^{s i n (3 x) l n (sech (2 x))}

= \frac{d}{d x} (e^{s i n (3 x) l n (sech (2 x))})

連鎖法則を適用:

e^{s i n (3 x) l n (sech (2 x))} \frac{d}{d x} (sin (3 x) ln (sech (2 x)))

= e^{s i n (3 x) l n (sech (2 x))} \frac{d}{d x} (sin (3 x) ln (sech (2 x)))

\frac{d}{d x} (sin (3 x) ln (sech (2 x))) = 3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x)

= e^{s i n (3 x) l n (sech (2 x))} (3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x))

e^{s i n (3 x) l n (sech (2 x))} = sech^{s i n (3 x)} (2 x)

= sech^{s i n (3 x)} (2 x) (3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x))