Chapter 3: Worksheet 3 Jack K. Cohen Colorado School of Mines
Techniques of Differentiation: Product and Quotient Rules
Suggested Problems Section 3.2: See below.
For the next few days, your job is get some mechanics well in hand. It is not practical to use a computer for every routine calculation! However, in the Colorado School of Mines calculus environment, you can make your learning more efficient by getting instant feedback on the accuracy of hand calculation of derivatives.
(* Take a simple derivative with Mma *) D[x^3 + 3x, x] 2 3 + 3 x (* Put in problem 3.2.25, but change variable to "t" *) g[t_] := (1/t - 2/t^2) / (2/t^3 - 3/t^4) D[g[t], t] (* Ask for derivative *) 4 -2 12 6 -2 1 -- - t (-- - --) (-- + -) 3 5 4 2 t t t t t -------- - ------------------ -3 2 -3 2 2 -- + -- (-- + --) 4 3 4 3 t t t t (* What a mess! Fortunately Mma has a Simplify function. The symbol % used in the next line means "previous output" *) Simplify[%] 2 t (12 - 13 t + 4 t ) -------------------- 2 (-3 + 2 t) (* If we anticipate the need for Simplify, we can do it all in one step. Reminder: g[] has been defined as a true function, so we can change the variable to x if we like *) Simplify[ D[g[x], x] ] 2 x (12 - 13 x + 4 x ) -------------------- 2 (-3 + 2 x) (* Mma also understands the prime notation for derivative. *) Simplify[ g'[t] ] 2 t (12 - 13 t + 4 t ) -------------------- 2 (-3 + 2 t)