DERIVATIVES

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1. If f(x) = 2x + 3, use the definition of derivative to find and then enter the rule for the derivative at x = a:

2.
Let f(x) =   __
x
 






By using the definition of derivative, find and enter the derivative at x = 1 (numerator followed by denominator). Sketch the graph and show the tangent line at x = 1.

3.  Using the derivative rules, find and enter the slope of the tangent line at x = 1 if f(x) = x2 + 2x +5. Sketch the graph and the tangent line on the same axes.



4. If     f(x) =
  __
x
 

1 + x2
    find the slope of the tangent   line at (1, 1
2
)









 


5. If     y =




1
   __
3x2
 





    Find     y (1)







6. At what point in Quadrant I is the line 3x + y = 0 parallel to a tangent line to xy = 12? Enter the point in the form (a,b). Sketch the graph and the tangent line.

 

7. 

Find y (-1)     if     y = xex-1








8.     Let     y(x) = ln|cos2x|     for 0 x p.     Find     y ( p
2
)








9. First, find the 2d derivative of     y = e-tsint. Is it true that y + 2y + 2y = 0?




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