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人気のある微分積分 >

derivative 4x^{10x^3}

解

導関数

4 x^{10 x^{3}}

解

40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

解答ステップ

\frac{d}{d x} (4 x^{10 x^{3}})

定数を除去:

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

= 4 \frac{d}{d x} (x^{10 x^{3}})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

x^{10 x^{3}} = e^{10 x^{3} l n (x)}

= 4 \frac{d}{d x} (e^{10 x^{3} l n (x)})

連鎖法則を適用:

e^{10 x^{3} l n (x)} \frac{d}{d x} (10 x^{3} ln (x))

= e^{10 x^{3} l n (x)} \frac{d}{d x} (10 x^{3} ln (x))

\frac{d}{d x} (10 x^{3} ln (x)) = 10 (3 x^{2} ln (x) + x^{2})

= 4 e^{10 x^{3} l n (x)} \cdot 10 (3 x^{2} ln (x) + x^{2})

簡素化

4 e^{10 x^{3} l n (x)} \cdot 10 (3 x^{2} ln (x) + x^{2}) : 40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

= 40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

グラフ

人気の例

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