Differentiation Rules Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Find the first derivative and the second derivative given

(2) Find the first derivative and the second derivative given

(3) Find the first derivative and the second derivative given

(4) Find the first derivative and the second derivative given

(5) Find the first derivative and the second derivative given

(6) Find the first derivative and the second derivative given

(7) Find the first derivative and the second derivative given

(8) Find the first derivative and the second derivative given

(9) Find the first derivative and the second derivative given

(10) Find the derivatives of all orders of the function given by

(11) Find the derivatives of all orders of the function given by   

(12) Find the derivatives of all orders of the function given by    

(13) Find the derivatives of all orders of the function given by    

(14) Find the derivatives of all orders of the function given by     

(15) Suppose and are differentiable functions of and that and Find the values of and at   

(16) (a) Find an equation for the line perpendicular to the tangent to the curve at the point (b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope? (c) Find equations for the tangents to the curve at the points where the slope of the curve is 8.

(17) (a) Find equations for the horizontal tangents to the curve Also find equations for the lines that are perpendicular to these tangents at the points of tangency. (b)  What is the smallest slope on the curve? At what point on the curve does the curve have this slope? Find an equation for the line that is perpendicular to the curve's tangent at this point.

(18) The curve passes through the point and is tangent to the line at the origin. Find and

(19) The curves and have a common tangent line at the point   Find and

(20) If gas in a cylinder is maintained at a constant temperature the pressure is related to the volume by a formula of the form in which and are constants. Find

(21) Determine so that given

(22) Determine so that given

(23) Find the first, second, and third derivatives of the following functions.

    (a)

    (b)
    

(24) Show that the curve has no tangent lines with slope

(25) At what points on the curve is the tangent line parallel to the line

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