A-Level Maths: G5-02 Differentiation: Introducing Implicit Differentiation
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- Опубліковано 20 гру 2017
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Just out of curiosity, is there such a thing as implicit integration, could you integrate an implicit function in a similar way?
I think the closest thing you're looking for would be multivariable calculus. en.wikipedia.org/wiki/Multiple_integral#Introduction
It's not sure if it's exactly analogous to what you're looking for though. Otherwise you move into exact differential equations or numerical methods
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At 5:56 , how do you prove that this equation is true, we've only shown with some examples that it works for positive integer powers. Is there a formal proof for this?
I'll refer you here: math.stackexchange.com/questions/94570/implicit-differentiation-proof
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Hi Jack, I know the A-level spec is limited to first order implicit differentiation, but if d/dx(y^2) is 2y(dy/dx), then what leads to d2y/dx^2?
Well if d/dx(y) = dy/dx
Then d/dx( d/dx(y) ) = d/dx( dy/dx ) = d^2y/dx^2
If d/dx(y^2) = 2y*dy/dx
Then d/dx( d/dx(y^2) ) = d/dx( 2y*dy/dx )
then using the product rule:
2y*d^2y/dx^2 + 2(dy/dx)^2
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goat
d/dx(g(o(a(t(x))))) = d/dx(g(o(a(t(x))))) * d/dx(o(a(t(x)))) * d/dx(a(t(x))) * d/dx(t(x)) dy/dx
If that was what you wanted, you're welcome.
If you mistyped "great", thank you for giving me more practise of the chain rule anyway.
i still dont quite get why you'd keep the dy/dx, could you explain that again?
Beyond replaying the video to have me explain it again, I'm not sure I know which bit you're having difficulty with? Happy to help
@@TLMaths it's fine now, i get it. thank you. had to rewatch the video a bunch of times and go away and do a problem to figure it out. thanks for all the help
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4:39 i have trust issues i was fully expecting you to prove why d/dx(y^4) wasn't 4y^3dy/dx
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