What is the derivative of (ln(x)/(x^{12)}) ?

The derivative of (ln(x)/(x^{12)}) is (1-12ln(x))/(x^{13)}

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

The first derivative of (ln(x)/(x^{12)}) is (1-12ln(x))/(x^{13)}

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\frac{d}{d x} (\frac{ln ( x )}{x ^{12}})

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

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{12}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

Simplify

\frac{\frac{1}{x} x ^{12} - 12 x ^{11} ln ( x )}{( x ^{12} ) ^{2}} : \frac{1 - 12 ln ( x )}{x ^{13}}

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

\int sec^{4} (x) \cdot tan^{2} (x) d x

\int_{0}^{3} x^{2} - 3 x d x

\frac{d}{d x} (ln (\frac{x + 1}{x ^{2} + 1}))

\int_{1}^{8} 9 \frac{ln ( x )}{x ^{2}} d x

x^{x^{2}}, 1

What is the derivative of (ln(x)/(x^{12)}) ?
The derivative of (ln(x)/(x^{12)}) is (1-12ln(x))/(x^{13)}
What is the first derivative of (ln(x)/(x^{12)}) ?
The first derivative of (ln(x)/(x^{12)}) is (1-12ln(x))/(x^{13)}