In each case, we assume that f '(x) and g'(x) exist and A and B are constants The four rules listed above, together with the rule on differentiating constant functions and the power rule, provide us with techniques for differentiating any function that is expressible as a power or root of a quotient of polynomial functions The next series of. Math 314H Solutions to Homework # 1 1 Let = f1x;1x2;xx2g be a subset of P 2 (a) Prove that is a basis for P2 Let = f1;x;x2g be the standard basis for P2 and consider the linear transforma tion T P2!R3 de ned by T(f) = f , where f is the coordinate vector of f with respect to Now, is a basis for P2 if and only if T( ) =. X o K V B B4 4WD E5AT 0R E4 h ACBABLE(04 N05 `05 N05 ) ̃z C T C Y ƃz C } b ` O B X o K V B B4 4WD E5AT 0R E4 h ACBABLE ̏ ̃z C ( W / I v V ) ̊O a A A I t Z b g A APCD i s b ` j A n u a ̌ J Ǝԑ̂ƃ^ C O ʂ̒i Z o z C E } b ` O u c C ` v V ~ V l ̌ J B X o K V B B4 4WD E5AT 0R E4 h A ̃A ~ z C w ⎩ Ԃ̃h X A b v Ȃǂ̍ۂ̎Q l Ƃ Ă p ܂ B.
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