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人気のある微分積分 >

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

解

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

解

- 2 e^{x^{2} - y^{2}} y

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

= - 2 e^{x^{2} - y^{2}} y

人気の例

limit as x approaches-infinity of 1/(4x)

x \to - \infty lim (\frac{1}{4 x})

d/(dy)(x^{(1+y)})

\frac{d}{d y} (x^{(1 + y)})

derivative of (dy/(dx))+y=0

\frac{d}{d x} (\frac{d y}{d x}) + y = 0

limit as x approaches-1.8 of-3x+18.4

x \to - 1.8 lim (- 3 x + 18.4)

y^{^{'}} = e^{t + y}