What is the derivative of (ln(x))/(x^9) ?

The derivative of (ln(x))/(x^9) is (1-9ln(x))/(x^{10)}

What is the first derivative of (ln(x))/(x^9) ?

The first derivative of (ln(x))/(x^9) is (1-9ln(x))/(x^{10)}

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derivative of

\frac{ln ( x )}{x ^{9}}

\frac{1 - 9 ln ( x )}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{9}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{9} - \frac{d}{d x} ( x ^{9} ) ln ( x )}{( x ^{9} ) ^{2}}

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{\frac{1}{x} x ^{9} - 9 x ^{8} ln ( x )}{( x ^{9} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{9} - 9 x ^{8} ln ( x )}{( x ^{9} ) ^{2}} : \frac{1 - 9 ln ( x )}{x ^{10}}

= \frac{1 - 9 ln ( x )}{x ^{10}}

What is the derivative of (ln(x))/(x^9) ?
The derivative of (ln(x))/(x^9) is (1-9ln(x))/(x^{10)}
What is the first derivative of (ln(x))/(x^9) ?
The first derivative of (ln(x))/(x^9) is (1-9ln(x))/(x^{10)}