Theory question 104
DifferentiationFind the gradient of xy2 + x2y = 4xy at the point (1, 3).
Show the model answer
Model answer
y² + 2xy(dy/dx) + 2xy + x²(dy/dx) = 4y + 4x(dy/dx).
At (1, 3): 9 + 6y′ + 6 + y′ = 12 + 4y′, so 3y′ = −3.
Gradient = −1.
Explanation
Differentiate each product with the product rule.