DERIVATIVES

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) = __ Ö 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) =
 __Ö x

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

5. If     y = æ
ç
ç
ç
ç
è
1
 __3Öx2
ö
÷
÷
÷
÷
ø
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?