Function closes

test/compute-engine/rubi-utils.test.ts:440–454

(latex: string)

describe('reverse chain rule — DerivativeDivides (4.7.5 #64–#67)', () => {
  // Rules pass ActivateTrig[y]/ActivateTrig[u]; pass active heads directly.
  const dd = (y: Json, u: Json): Expression =>
    build(['DerivativeDivides', y, u, 'x'] as Json, ctx);

  test('D(sin)=cos divides cos → 1 (∫cos·sin^m)', () => {
    expect(dd(['Sin', 'x'], ['Cos', 'x']).isSame(1)).toBe(true);
  });

  test('D(tan)=sec² divides sec² → 1 (∫sec²·tan^m)', () => {
    expect(dd(['Tan', 'x'], ['Power', ['Sec', 'x'], 2]).isSame(1)).toBe(true);
  });

  test('the wrong AC split returns the False symbol (not RuleFail)', () => {
    // y=cos, u=sin⁴: u/D(cos) = sin⁴/(−sin) = −sin³, not free of x
    expect(dd(['Cos', 'x'], ['Power', ['Sin', 'x'], 4]).symbol).toBe('False');
  });

  test('a bare linear y (a·x) is declined → False', () => {
    expect(dd(['Multiply', 2, 'x'], ['Cos', 'x']).symbol).toBe('False');