Is there a reason MuPad doesn't find the obvious cancellation?

I have:

f := 1/2* sqrt( 16-x^2 )

df := diff( f, x ) 

simplify( f * sqrt( 1 + df^2 ) )

mupad doesn't find the obvious cancellation (sqrt( 16-x^2 ) should go away)

Why not? Is there an algebraic reason I'm missing, or am I using the simplify function incorrectly, or is it something else?

Answer 1

[Matt Tearle]

I'm guessing it's something to do with assumptions about squares and square roots, and maybe denominators. Wouldn't swear to it, though. If you want it to do what you'd probably do by hand, you can try this:

Simplify(f * sqrt( 1 + df^2 ),IgnoreAnalyticConstraints)

(Note the capital S)

[Billy]

Thank you, this is a very nice feature (capital S- Simplify)

Answer 2

[Walter Roberson]

In particular sqrt(t) * sqrt(1/t) does not cancel if t is 0. Or in your case, if x = +/- 4