I can't access your link, can you type out the question?
Show that where
and also
Can anyone do? lol
p.s. This is the end simplification of another problem which I just don't know how to do.
Looking in particular to learn useful methods to do this efficiently for future reference.
Many thanks in advance!
Edit: Still need help...
Nup, this should definitely be true... unless my University maths professor made the mistake lol
Urm, its actually the end bit of another problem. Maybe you could do the full problem?:
Equation of a circle centre (1, -2) and radius 5 is given by
x^2-y^2-2x+4y-20=0
Show that (d^2.y)/(d.x^2 )=17/(2+y)^3
At the original post, the LHS is d^2y/dx^2, and a = dy/dx.
Hmm. I've moved this thread to Calculus, now that we're talking about second derivatives obtained implicitly. I get the following:
which appears to be your 'a'.
Using the quotient rule now, we get
As skeeter pointed out, the equation
is not a circle. It is an hyperbola, since the signs of the and terms are opposite.
I did my calculations in Post # 12 based on the (incorrect) hyperbola equation, not the (correct) circle equation exhibited by skeeter in post # 10. For the correct circle equation, I get the following:
and
The x's don't cancel, and I didn't think they would.
The fact it may be a circle or not is trivial in the question I think, but it's the "incorrect" equation we need to use.
For the equation of ,
I got:
which simplifies to:
and finally
I'm not sure if this is correct or not ,but it's how I did it... please elaborate
Edit:
For , I got the following:
SOMEHOW simplifies to:
Any idea how (3) simplifies to Middle section of (4)?