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人気のある微分積分 >

derivative of e^{x^2+y^2}

解

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

解

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

解答ステップ

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

連鎖法則を適用:

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

= e^{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}

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

人気の例

integral of x/(sqrt(x^2-100))

\int \frac{x}{x ^{2} - 100} d x

derivative of A*e^{-2x}*x

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

integral of (x^{3/2}+8x+2)

\int (x^{\frac{3}{2}} + 8 x + 2) d x

derivative of 2arctan(3x-ln(2+3x))

\frac{d}{d x} (2 arctan (3 x) - ln (2 + 3 x))

integral from 3 to 6 of 1/(sqrt(36-x^2))

\int_{3}^{6} \frac{1}{36 - x ^{2}} d x