Theory question 102
DifferentiationCalculate the gradient of the curve x3 + y3 − 2xy = 11 at the point (2, −1).
Show the model answer
Model answer
Differentiate implicitly: 3x² + 3y²(dy/dx) − 2y − 2x(dy/dx) = 0.
dy/dx = (2y − 3x²)/(3y² − 2x).
At (2, −1): (−2 − 12)/(3 − 4) = 14.
Explanation
Differentiate xy with the product rule.