derivative y=xln(x)cos(x)

解

導関数

y = x ln (x) cos (x)

ln (x) cos (x) + cos (x) - x sin (x) ln (x)

解答ステップ

\frac{d}{d x} (x ln (x) cos (x))

積の法則を適用:

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

f = x, g = ln (x) cos (x)

= \frac{d x}{d x} ln (x) cos (x) + \frac{d}{d x} (ln (x) cos (x)) x

\frac{d x}{d x} = 1

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

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

簡素化

1 \cdot ln (x) cos (x) + (\frac{cos ( x )}{x} - sin (x) ln (x)) x : ln (x) cos (x) + cos (x) - x sin (x) ln (x)

= ln (x) cos (x) + cos (x) - x sin (x) ln (x)