(\partial)/(\partial x)(cos(x^2+y^2-z))

解

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

- sin (x^{2} + y^{2} - z) \cdot 2 x

解答ステップ

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

y, z

を定数として扱う

連鎖法則を適用:

- sin (x^{2} + y^{2} - z) \frac{\partial}{\partial x} (x^{2} + y^{2} - z)

= - sin (x^{2} + y^{2} - z) \frac{\partial}{\partial x} (x^{2} + y^{2} - z)

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

= - sin (x^{2} + y^{2} - z) \cdot 2 x