What is the derivative of (ln(x))/(x^7) ?

The derivative of (ln(x))/(x^7) is (1-7ln(x))/(x^8)

What is the first derivative of (ln(x))/(x^7) ?

The first derivative of (ln(x))/(x^7) is (1-7ln(x))/(x^8)

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derivative of

\frac{ln ( x )}{x ^{7}}

\frac{1 - 7 ln ( x )}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{7}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ln ( x )}{( x ^{7} ) ^{2}}

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{\frac{1}{x} x ^{7} - 7 x ^{6} ln ( x )}{( x ^{7} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{7} - 7 x ^{6} ln ( x )}{( x ^{7} ) ^{2}} : \frac{1 - 7 ln ( x )}{x ^{8}}

= \frac{1 - 7 ln ( x )}{x ^{8}}

What is the derivative of (ln(x))/(x^7) ?
The derivative of (ln(x))/(x^7) is (1-7ln(x))/(x^8)
What is the first derivative of (ln(x))/(x^7) ?
The first derivative of (ln(x))/(x^7) is (1-7ln(x))/(x^8)