d/(dy)(e^{x^2-y^2}cos(2xy))

解

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

- 2 e^{x^{2} - y^{2}} y cos (2 x y) - 2 e^{x^{2} - y^{2}} x sin (2 x y)

解答ステップ

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

x

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x^{2} - y^{2}}, g = cos (2 x y)

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

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

\frac{d}{d y} (cos (2 x y)) = - sin (2 x y) \cdot 2 x

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

簡素化

= - 2 e^{x^{2} - y^{2}} y cos (2 x y) - 2 e^{x^{2} - y^{2}} x sin (2 x y)