What is the derivative of (ln(x))/(5x^3) ?

The derivative of (ln(x))/(5x^3) is (1-3ln(x))/(5x^4)

What is the first derivative of (ln(x))/(5x^3) ?

The first derivative of (ln(x))/(5x^3) is (1-3ln(x))/(5x^4)

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derivative of

\frac{ln ( x )}{5 x ^{3}}

\frac{1 - 3 ln ( x )}{5 x ^{4}}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( ln ( x ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ln ( x )}{( x ^{3} ) ^{2}}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{5} \cdot \frac{\frac{1}{x} x ^{3} - 3 x ^{2} ln ( x )}{( x ^{3} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{\frac{1}{x} x ^{3} - 3 x ^{2} ln ( x )}{( x ^{3} ) ^{2}} : \frac{1 - 3 ln ( x )}{5 x ^{4}}

= \frac{1 - 3 ln ( x )}{5 x ^{4}}

(4 x^{3} y^{2} - 6 x^{2} y - 2 x - 3) d x + (2 x^{4} y - 2 x^{3}) d y = 0

e^{- t} sin (3 t)

(\frac{2 y}{x} + 2 x) + \frac{( 2 ln ( x ) - 3 ) d y}{d x} = 0

n = 0 \sum \infty n^{2} (\frac{1}{2})^{n}

x \to 0 lim ((\frac{1}{x})^{t a n (x)})

What is the derivative of (ln(x))/(5x^3) ?
The derivative of (ln(x))/(5x^3) is (1-3ln(x))/(5x^4)
What is the first derivative of (ln(x))/(5x^3) ?
The first derivative of (ln(x))/(5x^3) is (1-3ln(x))/(5x^4)