Gabarito de Derivadas 53127

 O gabarito serve para você confirmar se acertou o processo de derivação. Caso sua resposta seja diferente do gabarito, examine sua solução de forma a detectar erros sutis que levaram a essa diferença.

Aqui estão as respostas para as questões:

1. ${�}^{\mathrm{\prime }}(�)=6�$
2. ${�}^{\mathrm{\prime }}(�)=\frac{1}{2\sqrt{�}}+6{�}^2$
3. ${ℎ}^{\mathrm{\prime }}(�)=-\frac{1}{{�}^2}+{�}^{�}$
4. ${�}^{\mathrm{\prime }}(�)=\frac{2{�}^3+3{�}^2-2}{{�}^2}$
5. ${�}^{\mathrm{\prime }}(�)=\frac{1}{�}+\cos (�)$
6. ${ℎ}^{\mathrm{\prime }}(�)=\frac{{�}^{�}(2-{�}^2)}{{�}^4}$
7. ${�}^{\mathrm{\prime }}(�)=16(2{�}^3+4�-1{)}^3(6{�}^2+4)$
8. ${�}^{\mathrm{\prime }}(�)=\frac{3�+1}{\sqrt{3{�}^2+2�+1}}$
9. ${ℎ}^{\mathrm{\prime }}(�)=\frac{-\sin (�)({�}^2+1)-2�\cos (�)}{({�}^2+1{)}^2}$
10. ${�}^{\mathrm{\prime }}(�)=\frac{6�+5}{3{�}^2+5�+2}$
11. ${�}^{\mathrm{\prime }}(�)=2{�}^{2�}\cos (�)-{�}^{2�}\sin (�)$
12. ${ℎ}^{\mathrm{\prime }}(�)=\frac{3{\sec }^2(�)-2\tan (�)}{{�}^4}$
13. ${�}^{\mathrm{\prime }}(�)=-\frac{1}{2�\sqrt{�}}-{�}^{-�}$
14. ${�}^{\mathrm{\prime }}(�)=0$
15. ${ℎ}^{\mathrm{\prime }}(�)=\frac{3{�}^2-2}{{�}^3-2�+1}$
16. ${�}^{\mathrm{\prime }}(�)=\frac{{�}^{�}(1-�)}{2{�}^{3\mathrm{/}2}}$
17. ${�}^{\mathrm{\prime }}(�)=3{\sec }^2(3�)$
18. ${ℎ}^{\mathrm{\prime }}(�)=\frac{2{�}^4+2�-2}{({�}^3+2�{)}^2}$
19. ${�}^{\mathrm{\prime }}(�)=\frac{{�}^{�}-\frac{1}{2}{�}^{-1\mathrm{/}2}{�}^{�}}{2\sqrt{�}{�}^{�}}$
20. ${�}^{\mathrm{\prime }}(�)=\frac{4�-3}{2{�}^2-3�+1}$
21. ${ℎ}^{\mathrm{\prime }}(�)=2�{�}^{{�}^2}\cos (�)-{�}^{{�}^2}\sin (�)$
22. ${�}^{\mathrm{\prime }}(�)=2\tan (�){\sec }^2(�)$
23. ${�}^{\mathrm{\prime }}(�)=\frac{�\cos (�)-\sin (�)}{{\cos }^2(�)}$
24. ${ℎ}^{\mathrm{\prime }}(�)=\frac{-2�}{({�}^2-1{)}^2}$
25. ${�}^{\mathrm{\prime }}(�)=\frac{{�}^{�}+\sqrt{�}{�}^{�}}{2\sqrt{�}}$
26. ${�}^{\mathrm{\prime }}(�)=\frac{\cos (�)}{\sin (�)}$
27. ${ℎ}^{\mathrm{\prime }}(�)=\frac{{�}^{�}(\cos (�)-2\sin (�))}{{\cos }^4(�)}$
28. ${�}^{\mathrm{\prime }}(�)=\frac{{\sec }^2(�)}{\sqrt{�}}+\frac{\tan (�)}{2\sqrt{�}}$
29. ${�}^{\mathrm{\prime }}(�)=\frac{�\cos (�)-\sin (�)({�}^2+1)}{({�}^2+1{)}^2}$
30. ${ℎ}^{\mathrm{\prime }}(�)=\frac{{�}^{\sqrt{�}}}{2\sqrt{�}}$
31. ${�}^{\mathrm{\prime }}(�)=\frac{6{�}^2-8�}{2{�}^3-4{�}^2+1}$
32. ${�}^{\mathrm{\prime }}(�)=-2\sin (2�)$
33. ${ℎ}^{\mathrm{\prime }}(�)=\frac{-2�\cos (�)-\sin (�)({�}^2-1)}{({�}^2-1{)}^2}$
34. ${�}^{\mathrm{\prime }}(�)=\frac{1+�}{{�}^2}{�}^{�}$
35. ${�}^{\mathrm{\prime }}(�)=\sqrt{�}(2{\sec }^2(2�)+\tan (2�))$
36. ${ℎ}^{\mathrm{\prime }}(�)=\frac{2{�}^{2�}-4�{�}^{2�}}{{�}^3}$
37. ${�}^{\mathrm{\prime }}(�)=\frac{{�}^{�}}{2\sqrt{{�}^{�}}}$
38. ${�}^{\mathrm{\prime }}(�)=\frac{-\sin (�)}{\cos (�)}$
39. ${ℎ}^{\mathrm{\prime }}(�)=\frac{-4�\cos (�)-\sin (�)({�}^2+4)}{({�}^2-4{)}^2}$
40. ${�}^{\mathrm{\prime }}(�)=\frac{\tan (�)+�{\sec }^2(�)}{{�}^{�}}$
41. ${�}^{\mathrm{\prime }}(�)=-\sin (�){�}^{\cos (�)}$
42. ${ℎ}^{\mathrm{\prime }}(�)=\frac{{�}^4-4{�}^3-3{�}^2-1}{({�}^4-1{)}^2}$
43. ${�}^{\mathrm{\prime }}(�)=\frac{\cos (�)}{2\sqrt{\sin (�)}}$
44. ${�}^{\mathrm{\prime }}(�)=\frac{\cos (�)}{\sin (�)}$
45. ${ℎ}^{\mathrm{\prime }}(�)=\frac{-2�\cos (�)-\sin (�)({�}^2+4)}{({�}^2+4{)}^2}$
46. ${�}^{\mathrm{\prime }}(�)=\frac{\ln (�)+1}{�{\cos }^2(�)}+\tan (�)\ln (�)$
47. ${�}^{\mathrm{\prime }}(�)=\frac{9{�}^2-6�+4}{2\sqrt{2{�}^3-3{�}^2+4�-1}}$
48. ${ℎ}^{\mathrm{\prime }}(�)={\sec }^2(�){�}^{\tan (�)}$
49. ${�}^{\mathrm{\prime }}(�)=\frac{{�}^{�}+\ln (�){�}^{�}}{2\sqrt{{�}^{�}}}$
50. ${�}^{\mathrm{\prime }}(�)=\frac{\cos (�)-\sin (�)}{\sin (�)+\cos (�)}$