derivative of cos(x^2+y^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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