# 15 calc questions

1.

If f(x) = 7x6cos-1x, find f ‘(x). (4 points)

 42x5cos-1x + 7x6 42x5cos-1x – 7x6 42x5cos-1x – 7x6cos-2x 42x5cos-1x + 7x6

2.

Find the derivative of e2x. (4 points)

 2xe2x 2e2x e2x 2ex

3.

If f(x) = ln(1 – 5x), then find f ‘(x). (4 points)

4.

Find . (4 points)

 e3lnx 3e3lnx 3x2

5.

For f(x) = ecos(x) use your graphing calculator to find the number of zeros for f ‘(x) on the closed interval [0, 2π]. (4 points)

 1 2 3 4

1.

Find y’ if x = tan(y). (4 points)

 cos2(y) sec2(y) 0 sin2(y)

2.

Find for x2 – y2 = xy. (4 points)

 2x – 2y 0

3.

If 3x2 + y2 = 7 then evaluate when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values. (4 points)

4.

Find if f(x) = (x + 2)7x. (4 points)

 7x(x + 2)(7x – 1) 7xln(x + 2)

5.

Find the slope of the graph of the relation 2x3 – 3xy + y3 = -1 at the point (2, -3). (4 points)

You may not use your calculator for these questions.



f

(

x

)

=

4.5

x

2

3

x

+

2

1. Use the limit definition to find f ′(x).
2. Use the alternate limit definition, with a = 2, to find the value of f ′(2).
3. Use the shortcut rules to find f ′(x).
4. Find where the tangent line to f(x) is horizontal.
5. Write the equation of the tangent line at x = 2.