Differentiation Core 3 Watch

Polymorphing
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#1
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Hi I have a couple of questions which I can't seem to do and need some help with, late night study ftw...

1. Find the points on the curve with equation 3x^2+y^2-2y=20 at which the gradient is 2.

2. Differentiate the implicit equation y^2=4x to find the gradient at (9,-6) on the curve.

3. Differentiate the implicit equation of the ellipse 3x^2+4y^2 = 16 to find the equation of the tangent at the point (2,-1)

Thanks in advance if you can show me the method to any of these questions.
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gyrase
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y^2 = 4x
=> y^2-4x=0
=> d/dx(y^2-4x) = 2y.y' - 4

sub (9,-6), 2(-6)y' - 4 = 0, y' = -1/3
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Swayum
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(Original post by gyrase)
y^2 = 4x
=> y^2-4x=0
=> d/dx(y^2-4x) = 2y.y' - 4
How does the second line imply the third line?
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122025278
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(Original post by Swayum)
How does the second line imply the third line?
Because y' is equal to d/dx(y) which is equal to dy/dx
He's just used that notation because its easier to write on the computer, is that the bit you didn't get?
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DoMakeSayThink
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(Original post by 122025278)
Because y' is equal to d/dx(y) which is equal to dy/dx
He's just used that notation because its easier to write on the computer, is that the bit you didn't get?
Actually, I think Swayum is pointing out a misuse of the 'implication' arrow.

y^2 - 4x = 0 does not imply that dy/dx(y^2-4x) = 2y.y' - 4

Correctly written, the argument would read:
 y^2 - 4x = 0 \\ \implies 2y\frac{dy}{dx} - 4 = 0
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gyrase
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The arrows I used were meant as lines of working rather than to signify implication.
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