derivative y=ln(x^8)

解答

导数

y = ln (x^{8})

\frac{8}{x}

求解步骤

\frac{d}{d x} (ln (x^{8}))

使用连锁律:

\frac{1}{x ^{8}} \frac{d}{d x} (x^{8})

= \frac{1}{x ^{8}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{x ^{8}} \cdot 8 x^{7}

化简

\frac{1}{x ^{8}} \cdot 8 x^{7} : \frac{8}{x}

= \frac{8}{x}

\frac{d y}{d x} = x^{5} (y - 3), y (0) = 5

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