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人気のある微分積分 >

derivative of (1+10^{ln(x})^6)

解

\frac{d}{d x} ((1 + 1 0^{l n (x)})^{6})

解

6 (1 + 1 0^{l n (x)})^{5} ln (10) x^{l n (10) - 1}

解答ステップ

\frac{d}{d x} ((1 + 1 0^{l n (x)})^{6})

連鎖法則を適用:

6 (1 + 1 0^{l n (x)})^{5} \frac{d}{d x} (1 + 1 0^{l n (x)})

= 6 (1 + 1 0^{l n (x)})^{5} \frac{d}{d x} (1 + 1 0^{l n (x)})

\frac{d}{d x} (1 + 1 0^{l n (x)}) = ln (10) x^{l n (10) - 1}

= 6 (1 + 1 0^{l n (x)})^{5} ln (10) x^{l n (10) - 1}

グラフ

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