Theory question 104
DifferentiationIf 3x2 + 2y2 + xy + x − 7 = 0, find dy/dx at the point (−2, 1).
Show the model answer
Model answer
Differentiate implicitly: 6x + 4y(dy/dx) + y + x(dy/dx) + 1 = 0
dy/dx = −(6x + y + 1)/(4y + x)
At (−2, 1): dy/dx = −(−12 + 1 + 1)/(4 − 2) = 10/2 = 5
Explanation
Use the product rule on the xy term.