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人気のある微分積分 >

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

解

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

解

e^{x^{5}} \cdot 5 x^{4}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

= e^{x^{5}} \cdot 5 x^{4}

人気の例

(\partial)/(\partial x)(x/((1-x)^2))

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

(\partial)/(\partial y)(1/(x^3-y^2))

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

tangent f(x)=x^2+3,\at x=1

t an g e n t f (x) = x^{2} + 3, at x = 1

limit as x approaches-10-of (x+9)/(x+10)

x \to - 10 - lim (\frac{x + 9}{x + 10})

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

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