Is this right?
Author
Hi all,
I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4
Now not quite sure what they were on about, but i did it this way. Just want to know if i worked it out right.
x^2 + y^2 -4 = 0
sqrt(4-x^2) = y
so
sub (4-x^2) with a letter, say u
sqrt(u) = y : y' = 1/2u^-1/2
u' = 4-x^2 : 2x
put it all back together and i got
y' = 1/2(sqrt(4-x^2)^-1/2) * 2x
which is the same as
y' = x*sqrt(4-x^2)^-1/2
Was I any where near right?
Thanks in advance.
You got: y' = x*sqrt(4-x^2)^-1/2
u' should be negative 2x right? and the ^-1/2 stands for sqrt(), so you should have
y' = -x/sqrt(4-x^2)
by my calculations.
I'm guessing you had x*(4-x^2)^-1/2 and you thought "beauty, 1/2 means sqrt()", and put your sqrt() in, forgetting to change the ^-1/2 to ^-1, which puts it on the denominator.
u' should be negative 2x right? and the ^-1/2 stands for sqrt(), so you should have
y' = -x/sqrt(4-x^2)
by my calculations.
I'm guessing you had x*(4-x^2)^-1/2 and you thought "beauty, 1/2 means sqrt()", and put your sqrt() in, forgetting to change the ^-1/2 to ^-1, which puts it on the denominator.
Be careful folks. This looks like schoolwork. Answer the question about whether the solution is basically correct, but do not provide detailed corrections! Remember, this forum is for game development math, not school!
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Quote:Original post by UK_Pablo
Hi all,
I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4
What does it mean to differentiate a formula?
Quote:Original post by alvaroQuote:Original post by UK_Pablo
Hi all,
I was searching for some info on the chain rule and came across an old post asking how to differentiate the following formula x^2 + y^2 = 4
What does it mean to differentiate a formula?
Not much, without saying which variable you are differentiating with respect to.
If you differentiate that formula with respect to z, or penguin, you get 0.
Well, in the most basic way, you can derive a formula without accounting for a particular variable.
for instance:
x = 5y + 2z2 + 5
dx = 5dy + 4zdz
is still a useful form.
for instance:
x = 5y + 2z2 + 5
dx = 5dy + 4zdz
is still a useful form.
That's not the tidiest way to calculate dy/dx. Note that the square-root function is not invertible (so you will have two solutions) and you have to perform a case-analysis on the sign of (4 - x²) if you're worried about getting complex solutions.
Implicit formulas don't, in general, give unique explicit expressions for derivatives. If the results are satisfactory, I highly recommend you look to implicit differentiation for a single-valued answer.
Regards
Admiral
Implicit formulas don't, in general, give unique explicit expressions for derivatives. If the results are satisfactory, I highly recommend you look to implicit differentiation for a single-valued answer.
Regards
Admiral
Quote:Original post by grhodes_at_work
Be careful folks. This looks like schoolwork. Answer the question about whether the solution is basically correct, but do not provide detailed corrections! Remember, this forum is for game development math, not school!
sorry mate
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