What is the derivative of (ln(x)/(x^{11)}) ?

The derivative of (ln(x)/(x^{11)}) is (1-11ln(x))/(x^{12)}

What is the first derivative of (ln(x)/(x^{11)}) ?

The first derivative of (ln(x)/(x^{11)}) is (1-11ln(x))/(x^{12)}

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\frac{d}{d x} (\frac{ln ( x )}{x ^{11}})

\frac{1 - 11 ln ( x )}{x ^{12}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{11}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{11} - \frac{d}{d x} ( x ^{11} ) ln ( x )}{( x ^{11} ) ^{2}}

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

\frac{d}{d x} (x^{11}) = 11 x^{10}

= \frac{\frac{1}{x} x ^{11} - 11 x ^{10} ln ( x )}{( x ^{11} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{11} - 11 x ^{10} ln ( x )}{( x ^{11} ) ^{2}} : \frac{1 - 11 ln ( x )}{x ^{12}}

= \frac{1 - 11 ln ( x )}{x ^{12}}

\frac{x ^{3}}{x ^{2} - 1}

k = 1 \sum \infty 0. 5^{k}

\int \frac{1}{4096} cos (8 x) d x

\frac{e ^{- 2 s}}{s - 1}

What is the derivative of (ln(x)/(x^{11)}) ?
The derivative of (ln(x)/(x^{11)}) is (1-11ln(x))/(x^{12)}
What is the first derivative of (ln(x)/(x^{11)}) ?
The first derivative of (ln(x)/(x^{11)}) is (1-11ln(x))/(x^{12)}