(\partial)/(\partial x)(sin(pi(3x-5y)))

解

\frac{\partial}{\partial x} (sin (π (3 x - 5 y)))

cos (π (3 x - 5 y)) \cdot 3 π

解答ステップ

\frac{\partial}{\partial x} (sin (π (3 x - 5 y)))

y

を定数として扱う

連鎖法則を適用:

cos (π (3 x - 5 y)) \frac{\partial}{\partial x} (π (3 x - 5 y))

= cos (π (3 x - 5 y)) \frac{\partial}{\partial x} (π (3 x - 5 y))

\frac{\partial}{\partial x} (π (3 x - 5 y)) = 3 π

= cos (π (3 x - 5 y)) \cdot 3 π