Is the quotient rule needed in this case?

Question

I need the partial derivative w.r.t. $r_{20}$, that in this function is only in the denominator, do I need to use the quotient rule?

$\dfrac{\partial f}{\partial r_{20}} = \dfrac{r_{00}*u/w + r_{01}*v/w+r_{02}/w+T_{0}}{r_{20}*u/w+r_{21}*v/w+r_{22}/w+T_{2}}$

Answer 1

Using the quotient rule is pretty trivial, since the partial derivative of the numerator will be zero.

Answer 2

You face the derivation problem of $y=\frac{u(x)}{v(x)}$ and you apply the quotient rule to get $$y'=\frac{u'(x)v(x)- u(x)v'(x)}{v^2(x)}$$ But, in your case $u(x)$ does not depend on $x$, so $u'(x)=0$. Then replacing, what is left is $$y'=\frac{- u(x)v'(x)}{v^2(x)}$$