What is the derivative of (1-2ln(x))/(x^3) ?

The derivative of (1-2ln(x))/(x^3) is -(-6ln(x)+5)/(x^4)

What is the first derivative of (1-2ln(x))/(x^3) ?

The first derivative of (1-2ln(x))/(x^3) is -(-6ln(x)+5)/(x^4)

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derivative of

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

- \frac{- 6 ln ( x ) + 5}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - 2 ln (x)) = - \frac{2}{x}

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

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

Simplify

\frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( 1 - 2 ln ( x ) )}{( x ^{3} ) ^{2}} : - \frac{- 6 ln ( x ) + 5}{x ^{4}}

= - \frac{- 6 ln ( x ) + 5}{x ^{4}}

\int \frac{64 - x ^{2}}{x ^{2}} d x

\int_{1}^{3} \frac{9}{x ^{2}} d x

\int e^{- 4 x} sin (5 x) d x

f (x) = \frac{110}{x ^{12}}

f (x) = 7 x^{4} arctan (4 x^{4})

What is the derivative of (1-2ln(x))/(x^3) ?
The derivative of (1-2ln(x))/(x^3) is -(-6ln(x)+5)/(x^4)
What is the first derivative of (1-2ln(x))/(x^3) ?
The first derivative of (1-2ln(x))/(x^3) is -(-6ln(x)+5)/(x^4)