Q: If f(r)=3 [r/(3^{1/2})]^{2 }(3r^{ -1})^{-1
}simplify this expression and find df/dr.

A: 3 [r/(3^{1/2})]^{2 }(3r^{ -1})^{-1 }
= 3 [r^{2}/3] r/3 = r^{3}/3. Thus df/dr = 3r^{2}/3
= r^{2}.

Answer to 2 point bonus question about the Simpsons:

After Bart switches IQ tests with the smart kid, his new teacher at the school
for talented and gifted kids gives this a problem and all of the other kids get
the joke. Notice that df = r^{2} dr or r dr r (har de har har).