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Assignments

Differentiate the following functions.

1.  y=x\sin(x)

Solution

2. y=(x^2+1)\ln(x)

Solution

3. y=2\sin(x)\cos(x)

Solution

4. y=e^x\ln(x)

Solution

5. y=3^x\sin(x)

Solution

6.  y=x.6^x

Solution

7. y=(x^3+x^2+1)\sin(x)

Solution

8. y=xe^x+e^x

Solution

9. y=\ln^2(x)

Solution

10. y=\sin^2(x)+\cos^2(x)

Solution

11. y=e^{2x}

Solution

12. y=\displaystyle\frac{1}{x-1}

Solution

13.  y=\displaystyle\frac{e^x}{x}

Solution

14. y=\tan(x)

Solution

15. y=\sin(2x)

Solution

16. y=\displaystyle\frac{\sin(x)}{x}

Solution

17. y=\displaystyle\frac{x^3+3}{x}

Solution

18. y=\displaystyle\frac{3}{x^2+1}

Solution

19. y=\displaystyle\frac{\ln(x)}{x}

Solution

20. y=\displaystyle\frac{xe^x+x^2}{x^2+1}

Solution

21. y=\displaystyle\frac{x^n+1}{x^n-1}, (n\neq0)

Solution

22.  y=\displaystyle\frac{x^2+5x+6}{x+3}

Solution

23. y=(x+6)(x-2)

Solution

24.  y=\displaystyle\frac{x+4}{x^2-16}

Solution

25. y=1-e^{-x}

Solution

26. y=e^{3x}

Solution

27. y=\displaystyle\frac{e^{3x}}{x^2+1}

Solution

28. y=\displaystyle\frac{\ln(x)}{\sqrt{x}}

Solution

29. y=1-\cos^2(x)

Solution

30.  y=\displaystyle\frac{(x+1)^2}{e^{2x}}

Solution

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