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could you implicitly differentiate that ?
you will need chain rule here whats d/dx x^2 =...? whats d/dx y^2=...?
what ? where does 2*2 come from ?
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) this is because of chain rule, got this step ?
d/dx (x^2) = 2x thats why and the other 2 was already there
ok, so now what about d/dx (x^2+y^2) =...?
here, chain rule again comes into picture d/dx f(y) = f'(y) dy/dx so d/dx (y^2) = 2y dy/dx got this ?
if you got that we are almost done :)
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) this part ?
whats d/dx x^2 =.... ?
we don't rewrite anything
derivative of outer times derivative of inner like for (sin x)^3 we have outer = x^3, derivative = 3x^2 inner = sin x derivative = cos x so, 3 (sin x)^2 cos x got this ?
in same way d/dx [(x^2+y^2)^2] = 2 (x^2+y^2) times d/dx (x^2+y^2)
i get that, but in this problem im confused with why the exponent goes away
ok, you said d/dx (x^2) = 2x why did the exponent go away here ?
so you're finding the derivative of the inside?
we do find derivative of inside in chain rule, right ?
my professor also taught us a way of outer first then rewrite inner and then multiple by the derivative of the inner.
he must have meant "derivative of outer first ....."
d/dx[f(g(x))]= f' (g(x))*g'(x)
yes, here f(x) was x2
well isn't it 4?
yes, it is 4.
oh so then it is. where are we getting x2?
d/dx[2(x^2+y^2)^2] = 2*(2 (x^2+y^2)) times d/dx(x^2+y^2) = 4(x^2+y^2)times d/dx(x^2+y^2)
sorry i didn't get your question?
got that =]
so can it be written like this? : d/dx 4(x^2+y^2) (2x+2y) ?
no, why would d/dx come in front again ?
so i get rid of it?
since i have the derivative already?
d/dx [(x^2+y^2)^2] = 2 (x^2+y^2) times d/dx (x^2+y^2) = 4 (x^2+y^2) times (2x+2y dy/dx) see whether you get this?
yeah i got it, but why don't we do dy/dx here: 4 (x^2+y^2) times (2x+2y dy/dx)|dw:1381774790286:dw|
we can't bc we have to leave it as it is right? according to the chain rule
because there, you have not differentiated x^2+y^2 yrt
and yes, we need to leave it as it is, that too
now what do we do
same for the other side?
yes, other side is too simple. try ?
right side is just 25(2x-2y dy/dx) isn't it ?
what why ? we need chain rule for just y^2 here, isn't it ?
huh i did?
its like 25x^2 - 25y^2 derivative = 25(2x) - 25 (2y dy/dx)
where did i go wrong?
the x^2-y^2 part was unnecessary, you though it was chain rule again ?
wait it wasn't because it had no exponent?
so its this?
now do we plug in x and y?
correct! put x=-3, y=1 in that...
i assume you are simplifying...
i don't know i keep getting the answer wrong whenever i try to submit it
what did u get for dy/dx ?
i keep getting incorrects :/
i got 3/119
4 (x^2+y^2) times (2x+2y dy/dx) = 25(2x-2y dy/dx) x=-3, y=1 4(9+1) (-6 +2 dy/dx) = 25 (-6 -2 dy/dx)
ohi wrote one of the signs wrong.
thank you so much!