Fall 2005 Math 229  Lab 9  Name:

1. Write each of the following functions as a composition of simpler functions.

(a) f(x) = (3x^{2} − 6x + 2)^{5}  (b) f(x) = (\sqrt{x} − 1)^{4}  (c) f(x) = \frac{1}{\sqrt{x^{4} − 1}}

2. Find and simplify (‘simplify’ means the factored form) the derivative of the following functions.

(a) y = (2x − 3)^{4} ; (b) R(x) = \sqrt{x^{4} + 4} ; (c) g(x) = (\frac{4x}{2x − 1})^{3}  {(d) f(x) = \frac{2x − 1}{\sqrt{x^{2} + 1}} \atop (e) y = (x^{2} + 2)^{4} (3x − 1)^{5}}

Show your work. Use correct notation. Give exact answers unless specified.

Fall 2005 Math 229  Lab 9  Name:

3. Find all derivatives of the function P (x) = 6x^{4} − x^{3} + 12x^{2} − 11x + 1.

4. Find the fourth derivative of y = \frac{x}{2x + 5}.

5. Do #67 in section 11.3.

6. Do #37 in section 11.5.

Show your work. Use correct notation. Give exact answers unless specified.