15 calc questions

1.

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


2.

Find the derivative of e2x. (4 points)



3.

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



4.

Find the derivative with respect to x of the quantity of e raised to the power of 3 times the natural log of x. . (4 points)



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.

Find y’ if x = tan(y). (4 points)


2.

Find dy, dx for x2 – y2 = xy. (4 points)



3.

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




4.

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



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, limit as x approaches a of the quantity f of x minus f of a over the quantity x minus a 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.