月下の棋士、大ピンチ！
>>551
(1)
f(t)=(√5)t^3
f'(t)=(2√5)t^2・・・答
(2)
f(u)=(u^2-u)^2
f'(u)=2(u^2-u)*(2u-1)=2u(u-1)(2u-1)・・・答
(3)
f(x)=q(x)*p(x)*r(rx)
f'(x)=q'(x)*p(x)*r(rx)+q(x)*p'(x)*r(rx)+q(x)*p(x)*r'(rx)*r
ゆえに，
f'(x)=p(x)*q'(x)*r(rx)+p'(x)*q(x)*r(rx)+r*p(x)*q(x)*r'(rx)・・・答
(4)
k(x)=q(x)･r(x)/p(x)
k'(x)=〔{q(x)*r(x)}'*p(x)-{q(x)*r(x)}*p'(x)〕/{p(x)}^2
ここで，{q(x)*r(x)}'=q(x)*r'(x)+q'(x)*r(x)
ゆえに
k(x)={p(x)*q(x)*r'(x)+p(x)*q'(x)*r(x)-p'(x)*q(x)*r(x)}/{p(x)}^2・・・答
(1)
f(t)=(√5)t^3
f'(t)=(2√5)t^2・・・答
(2)
f(u)=(u^2-u)^2
f'(u)=2(u^2-u)*(2u-1)=2u(u-1)(2u-1)・・・答
(3)
f(x)=q(x)*p(x)*r(rx)
f'(x)=q'(x)*p(x)*r(rx)+q(x)*p'(x)*r(rx)+q(x)*p(x)*r'(rx)*r
ゆえに，
f'(x)=p(x)*q'(x)*r(rx)+p'(x)*q(x)*r(rx)+r*p(x)*q(x)*r'(rx)・・・答
(4)
k(x)=q(x)･r(x)/p(x)
k'(x)=〔{q(x)*r(x)}'*p(x)-{q(x)*r(x)}*p'(x)〕/{p(x)}^2
ここで，{q(x)*r(x)}'=q(x)*r'(x)+q'(x)*r(x)
ゆえに
k(x)={p(x)*q(x)*r'(x)+p(x)*q'(x)*r(x)-p'(x)*q(x)*r(x)}/{p(x)}^2・・・答
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