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人気のある微分積分 >

derivative of (e^{(x^2}+4)^2)

解

\frac{d}{d x} ((e^{(x^{2})} + 4)^{2})

解

4 e^{x^{2}} x (e^{x^{2}} + 4)

解答ステップ

\frac{d}{d x} ((e^{(x^{2})} + 4)^{2})

連鎖法則を適用:

2 (e^{x^{2}} + 4) \frac{d}{d x} (e^{x^{2}} + 4)

= 2 (e^{x^{2}} + 4) \frac{d}{d x} (e^{x^{2}} + 4)

\frac{d}{d x} (e^{x^{2}} + 4) = 2 e^{x^{2}} x

= 2 (e^{x^{2}} + 4) \cdot 2 e^{x^{2}} x

簡素化

= 4 e^{x^{2}} x (e^{x^{2}} + 4)

グラフ

人気の例

y^{''}-8y^'+18y=0,y(0)=1,y^'(0)=-4

y^{^{''}} - 8 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

integral of (8x^2+5)^{10}x

\int (8 x^{2} + 5)^{10} x d x

integral of 2x(x^2+7)^7

\int 2 x (x^{2} + 7)^{7} d x

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\frac{d y}{d x} = - \frac{1}{3} x^{3}

(d^2)/(dx^2)(x+1/x)

\frac{d ^{2}}{d x ^{2}} (x + \frac{1}{x})