MediumCalculusca-025

Partial Derivatives of a Quadratic Form

Problem

For f(x, y) = a * x^2 + b * x * y + c * y^2, return the gradient [df/dx, df/dy] evaluated at (x, y).

df/dx = 2 * a * x + b * y and df/dy = b * x + 2 * c * y.

Hint

Treat the other variable as a constant when differentiating.

case 1

in: [1,2,3,1,2]

expected: [6,14]

case 2

in: [0,0,1,5,-3]

expected: [0,-6]

case 3

in: [2,-1,0,0,0]

expected: [0,0]

case 4

in: [1,1,1,-2,4]

expected: [0,6]

Starter codePython

def partial_derivatives(a, b, c, x, y):
    # Return [df_dx, df_dy]
    # Your code here
    pass

4 test cases · run your code against them in the editor