Derivatives worksheet with ten problems for calculating derivatives using the definition.

1) $ y' = 5(2x^3 + 2x)^4 \cdot (6x^2 + 2) $

2) $ y' = \frac{(3x^2 + 8x + 4)(4x^2 - 5) - (x^3 + 4x^2 + 4x)(8x)}{(4x^2 - 5)^2} $

3) $ y' = 3(5x^3 + 3x)^2 \cdot (15x^2 + 3) $

4) $ y' = 2x - 3 $

5) $ y' = \frac{(2x + 8)(3x^2 + 3x) - (x^2 + 8x + 8)(6x + 3)}{(3x^2 + 3x)^2} $

6) $ y' = 3x^2 - 9 $

7) $ y' = -2 \cdot (-\sin(-5x - 20)) \cdot (-5) = -10 \sin(-5x - 20) $

8) $ y' = 2 \cdot \sec^2(8x + 40) \cdot 8 = 16 \sec^2(8x + 40) $

9) $ y' = 6 \cdot (-\sin(-x - 3)) \cdot (-1) = 6 \sin(-x - 3) $

10) $ y' = 3x^2 - 2x - 9 $