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人気のある微分積分 >

(\partial)/(\partial x)(e^{5xy})

解

\frac{\partial}{\partial x} (e^{5 x y})

解

e^{5 x y} \cdot 5 y

解答ステップ

\frac{\partial}{\partial x} (e^{5 x y})

y

を定数として扱う

連鎖法則を適用:

e^{5 x y} \frac{\partial}{\partial x} (5 x y)

= e^{5 x y} \frac{\partial}{\partial x} (5 x y)

\frac{\partial}{\partial x} (5 x y) = 5 y

= e^{5 x y} \cdot 5 y

人気の例

integral of (sqrt(x))/(\sqrt[3]{x)}

\int \frac{x}{3 x} d x

derivative of sec^2(xtan^2(x))

\frac{d}{d x} (sec^{2} (x) tan^{2} (x))

integral of (2x+4)/(x^2-x)

\int \frac{2 x + 4}{x ^{2} - x} d x

(\partial)/(\partial x)(1/3 x^{3/2})

\frac{\partial}{\partial x} (\frac{1}{3} x^{\frac{3}{2}})

(\partial)/(\partial y)(6xcos(x)cos(y))

\frac{\partial}{\partial y} (6 x cos (x) cos (y))