(\partial)/(\partial y)(9x^y+2y^x+11)

解

\frac{\partial}{\partial y} (9 x^{y} + 2 y^{x} + 11)

2 x y^{x - 1} + 9 x^{y} ln (x)

解答ステップ

\frac{\partial}{\partial y} (9 x^{y} + 2 y^{x} + 11)

x

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 y} (9 x^{y}) + \frac{\partial}{\partial y} (2 y^{x}) + \frac{\partial}{\partial y} (11)

\frac{\partial}{\partial y} (9 x^{y}) = 9 x^{y} ln (x)

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

\frac{\partial}{\partial y} (11) = 0

= 9 x^{y} ln (x) + 2 x y^{x - 1} + 0

簡素化

= 2 x y^{x - 1} + 9 x^{y} ln (x)