MediumCalculusca-167

Implicit Function Theorem Slope

Problem

The curve x^a * y^b = c defines y implicitly as a function of x for x, y > 0.

By the implicit function theorem, dy/dx = -F_x / F_y = -a*y / (b*x). Given a, b > 0 and the point (x, y), return that slope.

Hint

Differentiate F(x, y) = x^a y^b - c partially with respect to each variable.

case 1

in: [2,3,1,2]

expected: -1.3333333333333333

case 2

in: [1,1,3,4]

expected: -1.3333333333333333

case 3

in: [1,2,2,1]

expected: -0.25

case 4

in: [3,3,1,1]

expected: -1

Starter codePython

def implicit_slope_power(a, b, x, y):
    # Your code here
    pass

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