Determine an equation of the tangent line to y e-3x at 0 1

Question

1. Find the derivative:  f(x) = ln (x + √(x² + 1))

2. Differentiate:  y = x^tan(x)  

3. Find dy/dx if x e^y + 1 = xy

4. Determine an equation of the tangent line to y = e^-3x at (0, 1)

5. Differentiate the implicit function 2ye^x + 1 = x 

6. Locate any relative extrema and points of inflection for f(x) = x²ln(x)

7. Find an equation of the tangent line at the point where x = 2 for the function: y = arctan(x/2)

8. Evaluate: ₂∫^e+1 1/x-1 dx

9. Evaluate: ∫(5/x²+6x+13)dx

10. Evaluate: _e∫^{e^2} 1/x dx  

11. Evaluate: ∫(4e^x/e^2x + 1)dx

12. Evaluate: ∫(3x² + 3x + 3/x² + 1) dx   

13. Without graphing the function, explain how you would determine whether f(x) = x-2/3 is 1-1. 

14. Solve: 3e^-2x = 6

15. Solve: ln(x) + ln(x-3) = 0.