x^2 - 5xy + 3y^2 = 7
We need to differentiate the equation with respect to x.
==> dy/dx( x^2 - 5xy + 3y^2 ) = dy/dx ( 7)
==> dy/dx (x^2) - 5 dy/dx ( xy) + dy/dx ( 3y^2) = dy/dx ( 7).
We will differentiate with respect to x.
==> 2x - 5 ( 1*y + xy' ) + 6yy' = 0
==> 2x - 5y - 5xy'+ 6yy' = 0
Now we will combine the terms with y' on the left side.
==> 6yy' - 5xy' = 5y - 2x
Now we will factor y'.
==> y'*( 6y - 5x ) = 5y-2x
Now we will divide by (6y-5x).
==> y' = (5y-2x)/(6y-5x)
Videos
We are given the equation x^2-5xy+3y^2=7 and we have to find dy/dx.
Differentiating each term of x^2 - 5xy + 3y^2 = 7 with respect to x, we get
2x - 5x(dy/dx)- 5y + 6y(dy/dx) = 0
taking the terms with dy/dx to one side and the other terms to the opposite side we get
=> 2x - 5y = (dy/dx)( 5x - 6y)
divide both the sides by 5x - 6y
=> (dy/dx) = (2x - 5y) / ( 5x - 6y)
Therefore (dy/dx) = (2x - 5y) / ( 5x - 6y)
We’ll help your grades soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support
Already a member? Log in here.
Are you a teacher? Sign up now