(\partial)/(\partial x)(ln(y)*ln(x^2+1))

解

\frac{\partial}{\partial x} (ln (y) \cdot ln (x^{2} + 1))

\frac{2 x ln ( y )}{x ^{2} + 1}

解答ステップ

\frac{\partial}{\partial x} (ln (y) ln (x^{2} + 1))

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (y) \frac{\partial}{\partial x} (ln (x^{2} + 1))

連鎖法則を適用:

\frac{1}{x ^{2} + 1} \frac{\partial}{\partial x} (x^{2} + 1)

= \frac{1}{x ^{2} + 1} \frac{\partial}{\partial x} (x^{2} + 1)

\frac{\partial}{\partial x} (x^{2} + 1) = 2 x

= ln (y) \frac{1}{x ^{2} + 1} \cdot 2 x

簡素化

ln (y) \frac{1}{x ^{2} + 1} \cdot 2 x : \frac{2 x ln ( y )}{x ^{2} + 1}

= \frac{2 x ln ( y )}{x ^{2} + 1}