(\partial)/(\partial x)(5x^2+y+sin(axy)+3)

解

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

a y cos (a x y) + 10 x

解答ステップ

\frac{\partial}{\partial x} (5 x^{2} + y + sin (a x y) + 3)

a, y

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} (5 x^{2}) + \frac{\partial}{\partial x} (y) + \frac{\partial}{\partial x} (sin (a x y)) + \frac{\partial}{\partial x} (3)

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

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

\frac{\partial}{\partial x} (3) = 0

= 10 x + 0 + cos (a x y) a y + 0

簡素化

= a y cos (a x y) + 10 x