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人気のある微分積分 >

(\partial)/(\partial x)(e^x-x(sin(y)))

解

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

解

e^{x} - sin (y)

解答ステップ

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

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (x sin (y)) = sin (y)

= e^{x} - sin (y)

人気の例

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\frac{d}{d x} (- x - 1)

limit as x approaches+1 of (1-x)/(x^2-1)

x \to + 1 lim (\frac{1 - x}{x ^{2} - 1})

integral from 0 to 1 of xe^{-6x^2}

\int_{0}^{1} x e^{- 6 x^{2}} d x

(\partial)/(\partial x)(e^{-7t}cos(pix))

\frac{\partial}{\partial x} (e^{- 7 t} cos (π x))