APPM 1340 Midterm: appm1340fall2017exam3_sol
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Fall 2017: [24 pts] for the given function, nd the indicated derivative. Simplify your nal answers, writing them without fractional and/or negative exponents: p(t) = + 2 7, p (t: y( ) = sin(cos 6 ), y (cid:16) . 4(cid:17: f (x) = xpx2 + 2, f (x) Solution: (a) p(t) = (3 t) 1/2 + 2 7 = p (t) = (b) y ( ) = cos(cos 6 )(cos 6 ) = cos(cos 6 )( sin 6 )(6 ) = 6(sin 6 ) cos(cos 6 )) implying that (3 t) 3/2( 1) + 0 = 2 (cid:19)(cid:21) = 6( 1) cos 0 = 6 (c) we can rewrite the original function as f (x) = x(x2 + 2)1/2 so that f (x) = x(cid:20) 1. = (x2 + 2) 1/2(cid:2)x2 + (x2 + 2)(cid:3) = (x2 + 2) 1/2(2x2 + 2) =
