(\partial)/(\partial x)(arcsin(3x+y))

解

\frac{\partial}{\partial x} (arcsin (3 x + y))

\frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}

解答ステップ

\frac{\partial}{\partial x} (arcsin (3 x + y))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{1 - ( 3 x + y ) ^{2}} \frac{\partial}{\partial x} (3 x + y)

= \frac{1}{1 - ( 3 x + y ) ^{2}} \frac{\partial}{\partial x} (3 x + y)

\frac{\partial}{\partial x} (3 x + y) = 3

= \frac{1}{1 - ( 3 x + y ) ^{2}} \cdot 3

簡素化

\frac{1}{1 - ( 3 x + y ) ^{2}} \cdot 3 : \frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}

= \frac{3}{1 - 9 x ^{2} - 6 x y - y ^{2}}