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人気のある微分積分 >

derivative of sin(2x^2*e^{-x})

解

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

解

cos (2 x^{2} e^{- x}) \cdot 2 (2 e^{- x} x - e^{- x} x^{2})

解答ステップ

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

連鎖法則を適用:

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

= cos (2 x^{2} e^{- x}) \frac{d}{d x} (2 x^{2} e^{- x})

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

= cos (2 x^{2} e^{- x}) \cdot 2 (2 e^{- x} x - e^{- x} x^{2})

グラフ

人気の例

tangent f(x)=(x-2)(2x+3),\at x=0

t an g e n t f (x) = (x - 2) (2 x + 3), at x = 0

integral of (x-5)*sin(x)

\int (x - 5) \cdot sin (x) d x

integral of (sin(x)tan(x))/(9+sec^2(x))

\int \frac{sin ( x ) tan ( x )}{9 + sec ^{2} ( x )} d x

t^2y^{''}+21ty^'+100y=0

t^{2} y^{^{''}} + 21 t y^{^{'}} + 100 y = 0

limit as x approaches 2 of 5a+ax

x \to 2 lim (5 a + a x)