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derivative question?
If 4x^2 + 2xy + 3y = 9 then the value dy/dx at the point (2,-1) is?
The answer is -2 but I don't know how to get there.
3 Answers
- Sky - VhinLv 65 years agoFavorite Answer
by implicit differentiation, note: in the term 2xy, apply product rule
4x^2 + 2xy + 3y = 9
8x +2[x dy/dx + y(1)] + 3 dy/dx = 0
simplify
8x + 2x dy/dx + 2y + 3 dy/dx = 0
2x dy/dx + 3 dy/dx = -8x - 2y
dy/dx(2x + 3) = -8x - 2y
dy/dx = (-8x - 2y)/(2x + 3)
substitute x=2 and y=-1
dy/dx = (-8x - 2y)/(2x + 3)
dy/dx = (-8*2 - 2*-1)/(2*2 + 3) = (-16 + 2)/(4+3) = -14/7 = -2
- ?Lv 75 years ago
Option 1: 4x^2 + 2xy + 3y = 9 becomes y = -(4x^2 + 9)/(2x + 3) and differentiate. After this you can substitute for x.
Option 2: 4x^2 + 2xy + 3y = 9 becomes 8x + 2x(dy/dx) + 2y + 3(dy/dx) = 0, then manipulate to dy/dx = f(x,y) After this you can substitute for x and y.
- Mike GLv 75 years ago
8x+2y+2x*dy/dx+3*dy/dx = 0
16 - 2 + 4*dy/dx + 3*dy/dx = 0
7*dy/dx + 14 = 0
dy/dx = -14/7 = -2
