MAT1475 Calculus I Derivative worksheet with 28 problems requiring differentiation of various functions.

1. $f'(x) = 15x^4 - 15x^2$
2. $f'(x) = 2(x^3 + 2)^3(7x^3 + 4)$
3. $f'(x) = e^x(\sin(2x) + 2\cos(2x))$
4. $f'(x) = -2(4x^3 - 2x)^{-3}(12x^2 - 2)$
5. $f'(x) = -4\csc^2(x)\cot(x) + 4\sin(x)$
6. $f'(x) = \frac{2(1 - x^2)}{(1 + x^2)^2}$
7. $f'(x) = \frac{4x - 9}{x^4}$
8. $f'(x) = \frac{35}{2}x^{5/2}$
9. $f'(x) = \frac{10x^4 - 9x^2 - 3}{x^4}$
10. $f'(x) = \frac{15x}{\sqrt{3x^2 - 6}}$
11. $f'(x) = \frac{-60x^2}{(2x^3 - 1)^3}$
12. $f'(x) = 2x^2e^{2x}$
13. $f'(x) = \frac{2}{3\sqrt{1 - 4x^2}}$
14. $f'(x) = \frac{6(\tan^{-1}(2x))^2}{1 + 4x^2}$
15. $f'(x) = \frac{2x^{1/3}}{3} - \frac{2}{3x^{4/3}}$
16. $f'(x) = 2\sec^2(2x)$
17. $f'(x) = \sin(2x)\tan(x) + 2\cos(2x)\sec^2(x)$
18. $f'(x) = \frac{2^x \ln(2)}{1 + 4^x}$
19. $f'(x) = 4\left(6x - \sqrt{x^2 + 1}\right)^3\left(6 - \frac{x}{\sqrt{x^2 + 1}}\right)$
20. $f'(x) = \frac{\cos(x)}{\sin^2(x)} - \frac{2\cos(x)}{\sin^3(x)}$
21. $f'(x) = \frac{8x + 20x^3}{(4x^2 + 5x^4)\ln(3)}$
22. $f'(x) = 2(2x + 1)\sec^2(x) + 2\sec^2(x)\tan(x)$