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人気のある微分積分 >

derivative (0.9e^x)/(tan(x))

解

導関数

\frac{0.9 e ^{x}}{tan ( x )}

解

0.9 (e^{x} cot (x) - e^{x} csc^{2} (x))

解答ステップ

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

簡素化

\frac{0.9 e ^{x}}{tan ( x )} : 0.9 e^{x} cot (x)

= \frac{d}{d x} (0.9 e^{x} cot (x))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 0.9 \frac{d}{d x} (e^{x} cot (x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = cot (x)

= 0.9 (\frac{d}{d x} (e^{x}) cot (x) + \frac{d}{d x} (cot (x)) e^{x})

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

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

= 0.9 (e^{x} cot (x) + (- csc^{2} (x)) e^{x})

簡素化

= 0.9 (e^{x} cot (x) - e^{x} csc^{2} (x))

グラフ

人気の例

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\int_{6}^{8} \frac{6}{( x - 6 ) ^{3}} d x

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\frac{d}{d x} (\frac{x ^{3} + 1}{x ^{2} + 3})

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