Question

For \[v\ne0\], what is the derivative of \[\frac{u}{v}\]?

Options

• \[\left(\frac{u}{v}\right)'=\frac{u'}{v'}\]

• \[\left(\frac{u}{v}\right)'=\frac{u'v+uv'}{v^2}\]

• \[\left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v}\]

• \[\left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}\]

Answer 1

The quotient rule has numerator \[u'v-uv'\] and denominator \[v^2\]. The condition \[v\ne0\] is required for the quotient to be defined.