What is the derivative of (u/v)^2 ?

The derivative of (u/v)^2 is (2u)/(v^2)

What is the first derivative of (u/v)^2 ?

The first derivative of (u/v)^2 is (2u)/(v^2)

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derivative

\frac{2 u}{v ^{2}}

Solution steps

\frac{d}{d u} ((\frac{u}{v})^{2})

Treat

v

as a constant

Apply the chain rule:

2 \cdot \frac{u}{v} \frac{d}{d u} (\frac{u}{v})

= 2 \cdot \frac{u}{v} \frac{d}{d u} (\frac{u}{v})

\frac{d}{d u} (\frac{u}{v}) = \frac{1}{v}

= 2 \cdot \frac{u}{v} \cdot \frac{1}{v}

Simplify

2 \cdot \frac{u}{v} \cdot \frac{1}{v} : \frac{2 u}{v ^{2}}

= \frac{2 u}{v ^{2}}

What is the derivative of (u/v)^2 ?
The derivative of (u/v)^2 is (2u)/(v^2)
What is the first derivative of (u/v)^2 ?
The first derivative of (u/v)^2 is (2u)/(v^2)