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人気のある微分積分 >

(\partial)/(\partial x)(e^{1+x^2-y^2})

解

\frac{\partial}{\partial x} (e^{1 + x^{2} - y^{2}})

解

e^{1 + x^{2} - y^{2}} \cdot 2 x

解答ステップ

\frac{\partial}{\partial x} (e^{1 + x^{2} - y^{2}})

y

を定数として扱う

連鎖法則を適用:

e^{1 + x^{2} - y^{2}} \frac{\partial}{\partial x} (1 + x^{2} - y^{2})

= e^{1 + x^{2} - y^{2}} \frac{\partial}{\partial x} (1 + x^{2} - y^{2})

\frac{\partial}{\partial x} (1 + x^{2} - y^{2}) = 2 x

= e^{1 + x^{2} - y^{2}} \cdot 2 x

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