(\partial)/(\partial x)(x^2cos(xln(y)))

解

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

2 x cos (x ln (y)) - x^{2} sin (x ln (y)) ln (y)

解答ステップ

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

y

を定数として扱う

積の法則を適用:

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

f = x^{2}, g = cos (x ln (y))

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

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

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

= 2 x cos (x ln (y)) + (- sin (x ln (y)) ln (y)) x^{2}

簡素化

= 2 x cos (x ln (y)) - x^{2} sin (x ln (y)) ln (y)