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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (e^{6 x} + 3 (ln (2))^{2} e^{2 x} - e^{4 x} ln (8) - (ln (2))^{3})

3 x

f (x) = - 2 x^{4} + 8 x^{2}

x \to 0 lim (tan (π x))

\int \frac{1}{( 9 x ^{2} + 4 ) ^{2}} d x

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