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just differentiate each part so you get 16x + 26y(dy/dx) - 10y -10x(dy/dx)= 0
everytime you differntiate a y put in dy/dx after it, when differntiating the -10xy just use the product rule to get -10x(dy/dx)-10y.
to simplify take everything that isnt with dy/dx to get:-
26y(dy/x)-10x(dy/dx)=10y-16x,
take out a factor of dy/dx ont he lhs
dy/dx(26y-10x)=10y-26x
just bring it over to ther otehr side
dy/dx=(10y-26x)/(26y-10x)
Thats it i think although id get someone to check, im prone to making stupid mistakes.
everytime you differntiate a y put in dy/dx after it, when differntiating the -10xy just use the product rule to get -10x(dy/dx)-10y.
to simplify take everything that isnt with dy/dx to get:-
26y(dy/x)-10x(dy/dx)=10y-16x,
take out a factor of dy/dx ont he lhs
dy/dx(26y-10x)=10y-26x
just bring it over to ther otehr side
dy/dx=(10y-26x)/(26y-10x)
Thats it i think although id get someone to check, im prone to making stupid mistakes.
Goody1
dy/dx=(10y-16x)/(26y-10x)
dy/dx=(10y-16x)/(26y-10x)
Then just simplify to dy/dx = (5y-13x)/(13y-5x)
As a check:
13x2 + 13y2 - 10xy = 52
=> 26x + 26y(dy/dx) - [ 10x(dy/dx) + 10y ] = 0
=> 26x + 26y(dy/dx) - 10x(dy/dx) - 10y = 0
=> dy/dx(26y - 10x) + 26x - 10y = 0
=> dy/dx(26y - 10x) = 10y - 26x
=> dy/dx = (10y - 26x)/( 26y - 10x)
Which means I have the same as you bar you have a -16x not a -26x.
You differentiated 13x2 to 16x. It is 26x.
13x2 + 13y2 - 10xy = 52
=> 26x + 26y(dy/dx) - [ 10x(dy/dx) + 10y ] = 0
=> 26x + 26y(dy/dx) - 10x(dy/dx) - 10y = 0
=> dy/dx(26y - 10x) + 26x - 10y = 0
=> dy/dx(26y - 10x) = 10y - 26x
=> dy/dx = (10y - 26x)/( 26y - 10x)
Which means I have the same as you bar you have a -16x not a -26x.
You differentiated 13x2 to 16x. It is 26x.
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