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x xx the function. Now we xxxx xx find its derivative:
Now xx xxxxx xx find xxx xxxxxx of xxxx xxxxxxxxxx xx have xxxxxxxx conditions. Firslty all xxxxxxxxx of xxxxxxxxxx xxxx xx xxxxxxx xxxx zero:
Secondly, all xxxxxxxxxxxx must xx different xxxx zero.
xxxxxxxxx , x x , x are xxxxxx real xxx different xxxx zero.
The final domain of xxx xxxxxxxxx is xxx xxxxxxxxx xx xxx conditions. The xxxxxx xxxxxxxx xxx the xxxxx 4 xxxxxxxxxx xxx
Because xx greater than xxx other numbers xx conditions. In xxxxx words if the x must be xxxxxxx than xx 1, xx than it must xx greater than .
We xxxx exclude xxxx the xxxxxx xxx values of x xxxx xxxxxxxxxx 6-10. Since numbers 0, 1, 5, x xxx xxx xx the interval, xxxxx is xx xxxxx xx xxxxxxxxx xxxxx The xxxx number we xxxx exclude xx :
This is xxx xxxxx solution.
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𝑦 x log(log8(log7(log6(log5 𝑥xxxx Y xx the function. Now xx have to xxxx xxx derivative: 𝑑𝑦
𝑑𝑥
𝑑𝑦
𝑑𝑥 = 𝑦′ x xxxxxxxxxxxxxxxxxxxx 𝑥))) xxx xx 10 xxx [log8(log7(log6(log5 𝑥)))]′ = xxxxxxxxxxxxxxxxxxxx 𝑥xxx xxx xx xx xxx 1log7(log6(log5 𝑥xx xxx xx 8 xxxxxxxxxxxxxxx 𝑥xxx′ x xxxxxxxxxxxxxxxxxxxx 𝑥xxx xxx xx xx xxx xxxxxxxxxxxxxxx 𝑥)) xxx xx x ∙ 1log6(log5 𝑥x xxx xx x [log6(log5 𝑥)]′ x xxxxxxxxxxxxxxxxxxxx 𝑥))) ∙ ln xx xxx xxxxxxxxxxxxxxx 𝑥)) xxx ln x xxx 1log6(log5 𝑥x ∙ xx xx
∙ 1log5 𝑥 ∙ xx 6 xxxxx 𝑥]′ = 1log8(log7(log6(log5 𝑥xxx ∙ ln 10 xxx xxxxxxxxxxxxxxx 𝑥)) xxx ln x xxx 1log6(log5 𝑥) xxx ln x xxx xxxxx 𝑥 ∙ ln xx
∙ 1
𝑥 ∙ ln 5 xxx in xxxxx xx find the domain of xxxx xxxxxxxxxx xx xxxx xxxxxxxx xxxxxxxxxxx Firslty all arguments of xxxxxxxxxx must be
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