MathB.in - Share Mathematics with LaTeX and Markdown

1. $g\left(z\right)=\frac{z^{7}+5z^{6}-z^{3}}{z^{2}}$
2. $N\left(\theta\right)=\tan\left(\arctan\left(k\theta\right)\right)$
3. $s\left(y\right)=\sqrt[3]{\cos^{2}e^{-y^{2}}+3+\sin^{2}e^{-y^{2}}}$
4. $g\left(x\right)=\frac{x^{2}+\sqrt{x}+1}{x^{{3}/{2}}}$
5. $y\left(x\right)=\left(2^{x}\right)^{2}+\frac{2}{x^{3}}$
6. $z\left(x\right)=\ln\left(xe^{x^{3}}\right)$
7. $h\left(x\right)=xe^{\tan x}$ 
8. $w\left(\theta\right)=\frac{\theta}{\sin^{2}\theta}$ 
9. $r\left(\theta\right)=\cos\left(2\theta^{-5}\right)\cdot e^{\theta}$
10. $y\left(z\right)=z^{2}+\frac{1}{2z}$ 
11. $y\left(t\right)=\sin t\cdot\arcsin t$ 
12. $\rho\left(w\right)=e^{-{3}/{w^{4}}}\arcsin\left(\ln w\right)$ 
13. $h\left(r\right)=\left(\ln r+\frac{1}{r}\right)^{5}$ 
14. $\tau\left(\nu\right)=\left(e^{\nu}+\nu^{e}\right)^{12}$ 
15. $h\left(s\right)=\frac{4+s^{2}}{\sqrt{4-s^{2}}}$ 
16. $\Theta\left(\theta\right)=e^{3e^{\theta}}$ 
17. $u\left(\tau\right)=\sqrt{\left(\tau^{4}+\tau\right)\left(e^{\tau}-6\right)}$ 
18. $g\left(w\right)=\frac{5}{\left(a^{2}-w^{2}\right)^{2}}$ 
19. $y\left(x\right)=\arctan\left(e^{\pi}+e^{x}\right)$ 
20. $g\left(t\right)=t\cos\left(\sqrt{t}e^{t}\right)$ 
21. $q\left(t\right)=\left(te^{t}+1\right)^{{3}/{2}}$ 
22. $f\left(x\right)=\arccos\left(x^{2}-e^{3x}\right)$ 
23. $g\left(t\right)=t^{2}e^{\left(t+\sin t\right)}$ 
24. $y\left(x\right)=2^{x\sin x}\cos x$ 
25. $f\left(r\right)=\left(\tan2+\tan r\right)^{e}$ 
26. $g\left(\theta\right)=\cos\left(\tan\theta\right)$ 
27. $q\left(y\right)=\frac{\sqrt{y}}{y}-\sqrt{y^{2}+1}$ 
28. $j\left(x\right)=\cos x\cdot\arcsin x$ 
29. $f\left(x\right)=\sqrt{\frac{\sin x}{1-\cos x}}$
30. $x\left(t\right)=\frac{e^{t}\cdot\ln t+1}{\tan t}$ 
31. $f\left(x\right)=\ln\left(\sin x+\cos x\right)$ 
32. $y\left(t\right)=3t^{5}-5\sqrt{t}+\frac{7}{t}$ 
33. $q\left(x\right)=\left(1+2x+x^{3}\right)^{60}$ 
34. $g\left(t\right)=\frac{\ln t+t}{\ln t-t}$ 
35. $f\left(x\right)=\tan\left(\sin x\right)$ 
36. $f\left(x\right)=3^{x+e^{x}}$ 
37. $g\left(y\right)=e^{2e^{y^{3}}}$ 
38. $\tau\left(z\right)=e^{5z^{3}+3^{z}}\sqrt[6]{2-9z}$ 
39. $f\left(x\right)=\cos\left(\sin x\right)$ 
40. $\xi\left(t\right)=\arctan\left(\ln t\right)$ 
41. $y\left(r\right)=r^{2}e^{\sin r}$
42. $\clubsuit\left(\diamondsuit\right)=\tan^{6}e^{\diamondsuit}$
43. $f\left(w\right)=\ln\left(\cos\left(w-1\right)\right)$ 
44. $f\left(t\right)=\cos^{2}\left(3t+5\right)$ 
45. $g\left(t\right)=\left(3t^{2}+\pi\right)\left(e^{t}-4\right)$ 
46. $g\left(\theta\right)=\arcsin\left(e^{\theta}\right)$ 
47. $s\left(y\right)=\tan^{6}\left(3z\right)$ 
48. $k\left(y\right)=e^{y}\tan\left(y^{3}\right)$ 
49. $\zeta\left(\xi\right)=\arctan\left(\frac{92}{\xi}\right)$ 
50. $z\left(\theta\right)=\sin^{3}\theta$ 
51. $\Phi\left(\psi\right)=\cos\left(e^{\psi}\cdot\ln\psi\right)$
52. $f\left(x\right)=\sqrt{\frac{e^{x}}{1-\cos x}}$ 
53. $x\left(t\right)=\frac{e^{t}}{\tan t\cdot\ln t}$ 
54. $\Phi\left(\psi\right)=\cos\left(e^{\psi}\left(6\psi-3\right)\right)$ 
55. $g\left(t\right)=\left(t^{2}+5\right)^{3}\left(3t^{3}-2\right)^{2}$ 
56. $y\left(\theta\right)=\sqrt{\cos5\theta}+\sin^{2}6\theta$ 
57. $f\left(x\right)=\arctan\left(x^{2}+1\right)$ 
58. $p\left(x\right)=4\ln\left(\sin x-\pi^{6}\right)$ 
59. $u\left(\rho\right)=\frac{e^{\rho}}{1+e^{\rho}}$
60. $M\left(\alpha\right)=\tan^{2}\left(2+3\alpha\right)$ 
61. $f\left(x\right)=\left(4-x^{2}+2x^{3}\right)\left(6-4x+x^{7}\right)$ 
62. $y\left(x\right)=x^{2}e^{x^{2}}$ 
63. $s\left(w\right)=w^{5}-3w^{2}+\sqrt[3]{w}+\frac{1}{w}$ 
64. $h\left(\beta\right)=\cos\left(\cos\beta\right)$ 
65. $k\left(\alpha\right)=e^{\tan\left(\sin\alpha\right)}$ 
66. $p\left(\theta\right)=\frac{\sin\left(5-\theta\right)}{\theta^{2}}$ 
67. $y\left(w\right)=\left(\cos\left(w\right)\cdot\ln\left(5w\right)\right)^{-{3}/{4}}$ 
68. $f\left(\theta\right)=\frac{1}{1+e^{-\theta}}$ 
69. $y\left(x\right)=e^{x}\sin^{2}x$ 
70. $f\left(y\right)=\ln\left(\ln2y^{3}\right)$ 
71. $f\left(x\right)=\sin\left(\sin x\right)$ 
72. $w\left(r\right)=\frac{ar^{2}}{b+r^{3}}$ 
73. $h\left(x\right)=\left(\frac{1}{x}-\frac{1}{x^{2}}\right)\left(2x^{3}+4\right)$ 
74. $G\left(x\right)=\frac{\sin^{2}x+1}{\cos^{2}x+1}$ 
75. $h\left(s\right)=\frac{4-s^{2}}{\sqrt{4+s^{2}}}$ 
76. $j\left(\theta\right)=\sqrt{\theta^{5}-\sin\theta}$ 
77. $s\left(\theta\right)=\sin^{2}\left(3\theta-\pi\right)$ 
78. $f\left(t\right)=\ln\left(t^{2}+1\right)$ 
79. $R\left(\Theta\right)=\sqrt{\Theta}\cos\left(\Theta^{2}\right)$ 
80. $q\left(z\right)=\arccos\left(\ln z\right)$ 
81. $q\left(x\right)=\sqrt[60]{1+2x+x^{3}}$ 
82. $g\left(w\right)=5\left(4+w^{2}\right)^{-2}$ 
83. $g\left(s\right)=\sin\left(s\cos s\right)$ 
84. $\alpha\left(t\right)=\sqrt{t}\cos\left(t^{2}e^{2t}\right)$ 
85. $f\left(x\right)=\sqrt{\left(\ln x\right)^{2}+5}$ 
86. $f\left(x\right)=2^{x}\tan x$ 
87. $g\left(z\right)=e^{-{2}/{z^{3}}}$ 
88. $y\left(x\right)=e^{2x}\sin^{2}3x$ 
89. $h\left(\delta\right)=\cos\left(e^{\delta}+1\right)$ 
90. $g\left(y\right)=\left(y^{4}+e^{y}+\pi\right)^{20}$ 
91. $g\left(t\right)=t\cos\left(\sqrt{t}\right)$
92. $r\left(z\right)=e^{z\cos z}$
93. $r\left(z\right)=\sqrt{e^{z}\tan z}$
94. $T\left(\theta\right)=e^{e^{e^{\theta}}}$ 
95. $f\left(z\right)=\sqrt{5z}+5\sqrt{z}+\frac{5}{\sqrt{z}}-\sqrt{\frac{5}{z}}+\sqrt{5}$
96. $g\left(t\right)=\frac{t\ln t}{\sin t}$
97. $k\left(t\right)=t\arcsin\left(t\right)+\sqrt{1-t^{2}}$
98. $t\left(u\right)=\sqrt{e^{u^{2}}+1}$
99. $\Sigma\left(\sigma\right)=\sqrt[5]{\frac{4\sigma}{3\sigma^{5}-8\sigma}}$
100. $Z\left(t\right)=e^{\frac{\cos t\cdot\arcsin^{3}\left(t^{2}-1\right)+3\sin^{2}\left(e^{2t}\right)}{\ln\left(t^{2}+e^{t}\right)}}\cdot\left(3^{e^{\arctan t^{2}}}+\tan\left(e^{\frac{t^{2}-1}{t^{2}+1}}\right)\right)^{4}$
(This uses just about every rule in the book!)
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Fri, 15 Oct 2021 23:00 GMT