# 15 calc questions

1.

If f(x) = 7x^{6}cos^{-1}x, find f ‘(x). (4 points)

2.

Find the derivative of e^{2x}. (4 points)

3.

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

4.

Find . (4 points)

5.

For f(x) = e^{cos(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 for x^{2} – y^{2} = xy. (4 points)

3.

If 3x^{2} + y^{2} = 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)

5.

Find the slope of the graph of the relation 2x^{3} – 3xy + y^{3} = -1 at the point (2, -3). (4 points)

You may not use your calculator for these questions.

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