What is the derivative of (ln(x)/(x^6)) ?

The derivative of (ln(x)/(x^6)) is (1-6ln(x))/(x^7)

What is the first derivative of (ln(x)/(x^6)) ?

The first derivative of (ln(x)/(x^6)) is (1-6ln(x))/(x^7)

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\frac{d}{d x} (\frac{ln ( x )}{x ^{6}})

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

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{x ^{6}})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

= \frac{\frac{1}{x} x ^{6} - 6 x ^{5} ln ( x )}{( x ^{6} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{6} - 6 x ^{5} ln ( x )}{( x ^{6} ) ^{2}} : \frac{1 - 6 ln ( x )}{x ^{7}}

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

\frac{d}{d x} (2 x - 2)

\int \frac{x ^{2} - 484}{x} d x

\int_{1}^{3} (x^{2} + 2 x - 3) d x

\int x^{3} arcsin (x) d x

2.5 x^{2} + 0.36 + 4 (1.1 - x)

What is the derivative of (ln(x)/(x^6)) ?
The derivative of (ln(x)/(x^6)) is (1-6ln(x))/(x^7)
What is the first derivative of (ln(x)/(x^6)) ?
The first derivative of (ln(x)/(x^6)) is (1-6ln(x))/(x^7)