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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derivative of

\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}}

x \to \infty lim (0.99)

x y^{^{'}} = e^{- y}

\int e^{- 8 x} d x

y^{^{''}} + 36 y = 36 sin (6 t)

f (x) = x^{4} - 10 x^{2} + 9

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)