mathUse implicit differentiation if y= x^2-5xy+3y^2=7
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
To find the derivative dy/dx of y= x^2-5xy+3y^2 implicit differentiation can be used and differentiation carried out in the following way:
y= x^2-5xy+3y^2
dy/dx = 2x - 5*x*(dy/dx) - 5y + 6y*(dy/dx)
take all terms with dy/dx to one side
dy/dx + 5*x*(dy/dx) - 6y*(dy/dx) = 2x - 5y
=> dy/dx( 1 + 5x - 6y) = 2x - 5y
=> dy/dx = (2x - 5y)/(1 + 5x - 6y)
The derivative dy/dx = (2x - 5y)/(1 + 5x - 6y)
giorgiana1976 | College Teacher | (Level 3) Valedictorian
We'll differentiate with respect to x to get dy/dx:
(d/dx)( x^2-5xy+3y^2-7)=0
We'll differentiate each term of the algebraic sum:
(d/dx)( x^2) - (d/dx)5xy + (dy/dx)3y^2 = 0
2x - (5x*(dy/dx) + 5y) + 6y*(dy/dx) = 0
(dy/dx)(5x + 6y) = -2x + 5y
We'll divide by 5x + 6y both sides:
dy/dx = (5y - 2x)/(5x + 6y)