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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\frac{d}{d x} (\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}}

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)