(\partial)/(\partial x)(3xln(y)+yln(z)-4x)

解

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

3 ln (y) - 4

解答ステップ

\frac{\partial}{\partial x} (3 x ln (y) + y ln (z) - 4 x)

y, z

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 x ln (y)) + \frac{\partial}{\partial x} (y ln (z)) - \frac{\partial}{\partial x} (4 x)

\frac{\partial}{\partial x} (3 x ln (y)) = 3 ln (y)

\frac{\partial}{\partial x} (y ln (z)) = 0

\frac{\partial}{\partial x} (4 x) = 4

= 3 ln (y) + 0 - 4

簡素化

= 3 ln (y) - 4