(\partial)/(\partial x)(arcsin(7xyz))

解

\frac{\partial}{\partial x} (arcsin (7 x yz))

\frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}

解答ステップ

\frac{\partial}{\partial x} (arcsin (7 x yz))

y, z

を定数として扱う

連鎖法則を適用:

\frac{1}{1 - ( 7 x yz ) ^{2}} \frac{\partial}{\partial x} (7 x yz)

= \frac{1}{1 - ( 7 x yz ) ^{2}} \frac{\partial}{\partial x} (7 x yz)

\frac{\partial}{\partial x} (7 x yz) = 7 yz

= \frac{1}{1 - ( 7 x yz ) ^{2}} \cdot 7 yz

簡素化

\frac{1}{1 - ( 7 x yz ) ^{2}} \cdot 7 yz : \frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}

= \frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}