What is the derivative of ((x^2+11))/(x^3) ?

The derivative of ((x^2+11))/(x^3) is (-x^2-33)/(x^4)

What is the first derivative of ((x^2+11))/(x^3) ?

The first derivative of ((x^2+11))/(x^3) is (-x^2-33)/(x^4)

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derivative of

\frac{( x ^{2} + 11 )}{x ^{3}}

\frac{- x ^{2} - 33}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 11}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 11 ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x ^{2} + 11 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} (x^{2} + 11) = 2 x

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

= \frac{2 x x ^{3} - 3 x ^{2} ( x ^{2} + 11 )}{( x ^{3} ) ^{2}}

Simplify

\frac{2 x x ^{3} - 3 x ^{2} ( x ^{2} + 11 )}{( x ^{3} ) ^{2}} : \frac{- x ^{2} - 33}{x ^{4}}

= \frac{- x ^{2} - 33}{x ^{4}}

What is the derivative of ((x^2+11))/(x^3) ?
The derivative of ((x^2+11))/(x^3) is (-x^2-33)/(x^4)
What is the first derivative of ((x^2+11))/(x^3) ?
The first derivative of ((x^2+11))/(x^3) is (-x^2-33)/(x^4)