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

The derivative of-(-2ln(x+3)/(x^3)) is (-6ln(x)+11)/(x^4)

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

The first derivative of-(-2ln(x+3)/(x^3)) is (-6ln(x)+11)/(x^4)

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

\frac{- 6 ln ( x ) + 11}{x ^{4}}

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

- \frac{( - \frac{2}{x} ) x ^{3} - 3 x ^{2} ( - 2 ln ( x ) + 3 )}{( x ^{3} ) ^{2}} : \frac{- 6 ln ( x ) + 11}{x ^{4}}

= \frac{- 6 ln ( x ) + 11}{x ^{4}}

\frac{( 12 s + 3 )}{s ^{2} ( 2 s + 8 )}

\int \frac{1}{- x ^{- 2} + 2 x} d x

y^{^{'}} + \frac{y}{9.33} = 6.429

y^{^{''}} = x^{4}

\frac{s}{s + 3}

What is the derivative of-(-2ln(x+3)/(x^3)) ?
The derivative of-(-2ln(x+3)/(x^3)) is (-6ln(x)+11)/(x^4)
What is the first derivative of-(-2ln(x+3)/(x^3)) ?
The first derivative of-(-2ln(x+3)/(x^3)) is (-6ln(x)+11)/(x^4)