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Unformatted text preview: HW-2 SOLUTIONSec 1.22. (a) We differentiate the implicit function with respect to x, which yields:21dyydx .This is equivalent to 12dydxy , wherey.Furthermore, 23(,3)yxx .(b) The definition of the implicit function reduces to3(sin)1yxxx.By differentiating the previous equality with respect to x, we get:233(sin)(1sincos)dyyxxxyxxxdx.This is equivalent to (cossin1)3(sin)dyxxxydxxxx.3.Yes. The differentiation yields: cos2 ,dyxxdx22dsin2yxdx .Substituting these equalities into the equation from the book, we get: LHS =22sin2sin2xxxxRHS6.No. Since 3262ttdeedtand 2322184ttdeedt, we have: 232323232265432231842623 2121022472ttttttttttttttddeeeeeeeedtdteeeeee 10.Yes. Differentiation of 2ln1yyxyields: 12dydyxdxy dx, which is equivalent to 21dyxydxy....
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