MediumCalculusca-029

Chain Rule Evaluation

Problem

Evaluate the derivative of the composite f(g(x)) at x, where f(u) = u^3 + 2 * u and g is a polynomial given by coefficients.

By the chain rule, the derivative is (3 * g(x)^2 + 2) * g'(x).

Hint

Differentiate the outer function at g(x) and multiply by the inner derivative.

case 1

in: [[0,1],2]

expected: 14

case 2

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

expected: 200

case 3

in: [[3],5]

expected: 0

case 4

in: [[1,0,1],0]

expected: 0

case 5

in: [[0,0,0,1],1]

expected: 15

Starter codePython

def chain_rule(coeffs, x):
    # f(u) = u**3 + 2*u, g is the polynomial
    # Your code here
    pass

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