(\partial)/(\partial x)(sin(pi(5x-4y)))

解

\frac{\partial}{\partial x} (sin (π (5 x - 4 y)))

cos (π (5 x - 4 y)) \cdot 5 π

解答ステップ

\frac{\partial}{\partial x} (sin (π (5 x - 4 y)))

y

を定数として扱う

連鎖法則を適用:

cos (π (5 x - 4 y)) \frac{\partial}{\partial x} (π (5 x - 4 y))

= cos (π (5 x - 4 y)) \frac{\partial}{\partial x} (π (5 x - 4 y))

\frac{\partial}{\partial x} (π (5 x - 4 y)) = 5 π

= cos (π (5 x - 4 y)) \cdot 5 π