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

The derivative of (x^3+1)/(x^3) is -3/(x^4)

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

The first derivative of (x^3+1)/(x^3) is -3/(x^4)

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derivative of

\frac{x ^{3} + 1}{x ^{3}}

- \frac{3}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{3}{x ^{4}}

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