(\partial)/(\partial y)(sqrt(y+cos^2(x)))

解

\frac{\partial}{\partial y} (y + cos^{2} (x))

\frac{1}{2 y + cos ^{2} ( x )}

解答ステップ

\frac{\partial}{\partial y} (y + cos^{2} (x))

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

= \frac{1}{2 y + cos ^{2} ( x )}