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1.

The derivative of f(x) = 4 x³ - 5 x² + 7 x - 9 with respect to x is:

f'(x) = 4 x² - 5 x + 7

f'(x) = 12 x² - 10 x

f'(x) = 12 x³ - 10 x² + 7

f'(x) = 12 x² - 10 x + 7

2.

The slope of the tangent line to the curve y = x² - 6 x + 5 at the point (4, -3) equals:

m = -2

m = 2

m = -3

m = 8

3.

If y = (2x + 1) * (3x - 4), then dy/dx evaluated at x = 1 equals:

12

7

-5

1

4.

Using the Quotient Rule, the derivative of y = (x + 3) / (x - 2) for x != 2 is:

-5 / (x - 2)²

(2x + 1) / (x - 2)²

1 / (x - 2)²

5 / (x - 2)²

5.

According to the Chain Rule, if y = (3 x² - 5)⁴, then dy/dx is:

24 x (3 x² - 5)³

4 (3 x² - 5)³

6 x (3 x² - 5)³

12 x (3 x² - 5)⁴

Lesson 1 – Rate of Change and Differentiation Rules — Lesson quiz