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HW04 - MATH 132 HW 04 Answer Section 3.2[4 Find the first...

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MATH 132 HW 04 Answer Section 3.2 [4]. Find the first and second derivatives of w = 3 z 7 - 7 z 3 + 21 z 2 Solution: dw dz = w = 21 z 6 - 21 z 2 + 42 z d 2 w dz 2 = w = 126 z 5 - 42 z + 42 [8]. Find the first and second derivatives of s = - 2 t - 1 + 4 t 2 Solution: s = - 2 t - 1 + 4 t 2 = - 2 t - 1 + 4 t - 2 ds dt = s = 2 t - 2 - 8 t - 3 d 2 s dt 2 = s = - 4 t - 3 + 24 t - 4 [20]. Find the derivative of f ( t ) = t 2 - 1 t 2 + t - 2 Solution: f ( t ) = t 2 - 1 t 2 + t - 2 = ( t - 1)( t + 1) ( t - 1)( t + 2) = t + 1 t + 2 f ( t ) = ( t + 1) ( t + 2) - ( t + 1) ( t + 2) ( t + 2) 2 = 1 · ( t + 2) - ( t + 1) · 1 ( t + 2) 2 = 1 ( t + 2) 2 [28]. Find the derivative of
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