What is the derivative of (ln(x)/(x^{13)}) ?

The derivative of (ln(x)/(x^{13)}) is (1-13ln(x))/(x^{14)}

What is the first derivative of (ln(x)/(x^{13)}) ?

The first derivative of (ln(x)/(x^{13)}) is (1-13ln(x))/(x^{14)}

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\frac{d}{d x} (\frac{ln ( x )}{x ^{13}})

\frac{1 - 13 ln ( x )}{x ^{14}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{13}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{13} - \frac{d}{d x} ( x ^{13} ) ln ( x )}{( x ^{13} ) ^{2}}

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

\frac{d}{d x} (x^{13}) = 13 x^{12}

= \frac{\frac{1}{x} x ^{13} - 13 x ^{12} ln ( x )}{( x ^{13} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{13} - 13 x ^{12} ln ( x )}{( x ^{13} ) ^{2}} : \frac{1 - 13 ln ( x )}{x ^{14}}

= \frac{1 - 13 ln ( x )}{x ^{14}}

\frac{10}{x}

x \to a lim (\frac{x - 1}{3 x + 6})

\int (x ln (x)) d x

\frac{d}{d x} (π r (x) (x)^{2} h)

\frac{d y}{d x} = \frac{3 x}{2 y}

What is the derivative of (ln(x)/(x^{13)}) ?
The derivative of (ln(x)/(x^{13)}) is (1-13ln(x))/(x^{14)}
What is the first derivative of (ln(x)/(x^{13)}) ?
The first derivative of (ln(x)/(x^{13)}) is (1-13ln(x))/(x^{14)}