簡約 (d^2)/(d^2x)(e^{-2xy}*sin(x^2-y^2))

解

簡約

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

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

解答ステップ

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

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{2 x y}} \cdot \frac{d ^{2}}{d ^{2} x} sin (x^{2} - y^{2})

分数を乗じる:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{d ^{2} \cdot 1 \cdot sin ( x ^{2} - y ^{2} )}{d ^{2} x e ^{2 x y}}

共通因数を約分する:

d^{2}

= \frac{1 \cdot sin ( x ^{2} - y ^{2} )}{x e ^{2 x y}}

乗算:

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

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