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人気のある微分積分 >

(\partial)/(\partial y)(e^{xy^2})

解

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

解

e^{x y^{2}} \cdot 2 x y

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

= e^{x y^{2}} \cdot 2 x y

人気の例

integral from 1 to 2 of t^4f(t^5)

\int_{1}^{2} t^{4} f (t^{5}) d t

tangent y=5x^3-5x,(-1,0)

t an g e n t y = 5 x^{3} - 5 x, (- 1, 0)

inverselaplace (1000)/(s+1000)

in v erse l a pl a ce \frac{1000}{s + 1000}

derivative of (2sqrt(2)/(x^2))

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

derivative (3e^x)/((3+e^x)^2)

d er i v a t i v e \frac{3 e ^{x}}{( 3 + e ^{x} ) ^{2}}