MATH 231 Study Guide - Quiz Guide: Quotient Rule, Product Rule, Power Rule
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Due: tuesday, june 2: (computation of derivatives. ) Let g(x) = 3x 2 to compute g ( /3) . Use either the product rule or the quotient rule. Let us use the product rule, which states that if two functions u and v are being multiplied together, their derivative is given by (u v) = u . Here, let"s pick u = 3x 2, and v = cos(x). From the power rule, (3x 2) = 2 3x 3 = 6x 3. And, we have that (cos(x)) = sin(x). We then plug in /3: g (x) = 6x 3. Using the fact that x 2 = 1/x2, we equivalently have g(x) = We can then apply the quotient rule, which states for functions u and v that where we have u = 3 cos(x) and v = x2. Making this substitution, we see (cid:16) u v(cid:17) v u . U v v2 g (x) = x2. = 3x2 sin(x) 6x cos(x) x4.
