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implicit differentiation (1 Viewer)

shaon0

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can someone please show me how to derive x/y and x^2/y^2 w.r.t x


thank you
d/dx (x/y) = (y+xy')/y^2 [By quotient rule]

d/dx (x^2/y^2)
= d/dx ((x/y)^2)
= 2(x/y).d/dx (x/y) [By chain rule]
= 2x/y.(y+xy')/y^2
= 2x(y+xy')/y^3

Might be a problem in the solution.
Just treat it as a normal derivative but when differentiating y wrt x, let d/dx (y)=dy/dx=y'
 
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bob fossil

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d/dx (x/y) = (y+xy')/y^2 [By quotient rule]

d/dx (x^2/y^2)
= d/dx ((x/y)^2)
= 2(x/y).d/dx (x/y) [By chain rule]
= 2x/y.(y+xy')/y^2
= 2x(y+xy')/y^3

Might be a problem in the solution.
Just treat it as a normal derivative but when differentiating y wrt x, let d/dx (y)=dy/dx=y'


Thank you
 

bob fossil

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I know it's picky, but you actually "differentiate". Deriving is different.
i really need to learn the language lol i got the first letter right lol


can anyone make sence of what this question is asking?

The tangent at P(3, 3/2) on the curve 3y+xy-3x=0 cuts the y axis at T. The ordinate PG meets the x axis st G. show that:

[OG]^2=3xOT


found gradient.
found equation of tangent.
found T at 3,0
dont know how an ordinate can meet the x axis?
 

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