derivative sin(5xln(x))(sin^2(5x))

解

導関数

sin (5 x ln (x)) (sin^{2} (5 x))

cos (5 x ln (x)) \cdot 5 (ln (x) + 1) sin^{2} (5 x) + 5 sin (10 x) sin (5 x ln (x))

解答ステップ

\frac{d}{d x} (sin (5 x ln (x)) sin^{2} (5 x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (5 x ln (x)), g = sin^{2} (5 x)

= \frac{d}{d x} (sin (5 x ln (x))) sin^{2} (5 x) + \frac{d}{d x} (sin^{2} (5 x)) sin (5 x ln (x))

\frac{d}{d x} (sin (5 x ln (x))) = cos (5 x ln (x)) \cdot 5 (ln (x) + 1)

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= cos (5 x ln (x)) \cdot 5 (ln (x) + 1) sin^{2} (5 x) + 5 sin (10 x) sin (5 x ln (x))