derivative of cos^{ln(7x}(x))

解

\frac{d}{d x} (cos^{l n (7 x)} (x))

(\frac{ln ( cos ( x ) )}{x} - tan (x) ln (7 x)) (7 x)^{l n (c o s (x))}

解答ステップ

\frac{d}{d x} (cos^{l n (7 x)} (x))

指数の規則を適用する:

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

cos^{l n (7 x)} (x) = e^{l n (7 x) l n (c o s (x))}

= \frac{d}{d x} (e^{l n (7 x) l n (c o s (x))})

連鎖法則を適用:

e^{l n (7 x) l n (c o s (x))} \frac{d}{d x} (ln (7 x) ln (cos (x)))

= e^{l n (7 x) l n (c o s (x))} \frac{d}{d x} (ln (7 x) ln (cos (x)))

\frac{d}{d x} (ln (7 x) ln (cos (x))) = \frac{ln ( cos ( x ) )}{x} - tan (x) ln (7 x)

= e^{l n (7 x) l n (c o s (x))} (\frac{ln ( cos ( x ) )}{x} - tan (x) ln (7 x))

e^{l n (7 x) l n (c o s (x))} = (7 x)^{l n (c o s (x))}

= (\frac{ln ( cos ( x ) )}{x} - tan (x) ln (7 x)) (7 x)^{l n (c o s (x))}