implicit differentiation (1 Viewer)

[bob fossil]

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


thank you

 

[shaon0]

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'

 

[bob fossil]

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]

Thank you

Isn't it awesome when the answers are wrong on the back on your teachers handouts?

Thanks again

 

[bob fossil]

= 2(x/y).d/dx (x/y)

does this also = 2(x/y).xy

 

[shaon0]

does this also = 2(x/y).xy

Yeah, it should. I'm not entirely sure if my answers are correct though.

 

[jet]

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


thank you

I know it's picky, but you actually "differentiate". Deriving is different.

 

[gurmies]

I know it's picky, but you actually "differentiate". Deriving is different.

LOL, I had typed something similar to this, but then thought meh. Glad someone said it xD

 

[bob fossil]

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?