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

The derivative of (v^3+1)/v is (2v^3-1)/(v^2)

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

The first derivative of (v^3+1)/v is (2v^3-1)/(v^2)

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derivative of

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

\frac{2 v ^{3} - 1}{v ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d v}{d v} = 1

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

Simplify

\frac{3 v ^{2} v - 1 \cdot ( v ^{3} + 1 )}{v ^{2}} : \frac{2 v ^{3} - 1}{v ^{2}}

= \frac{2 v ^{3} - 1}{v ^{2}}

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