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maksim4k23
@maksim4k23
November 2021
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ВЫЧИСЛИТЬ ПРОИЗВОДНУЮ ФУНКЦИЙ
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zews1065
Verified answer
1. = (-3arcsinx)'+(4√2x)'=-3/√(1-x²)+4·2/2√2x=-3/√(1-x²)+2√2/x
2. =(1/6x⁶)'·(e∧6x+e∧-6x)+1/6x⁶·(e∧6x+e∧-6x)'=x⁵·(e∧6x+e∧-6x)+1/6x⁶·(6
e∧6x
-6e∧-6x
)=x⁵·(e∧6x+e∧-6x)+x⁶·
(e∧6x-e∧-6x)
3. =(x/2)'
·㏑(e∧-2x+xe∧-2x)+1/2x·[㏑(e∧-2x+xe∧-2x)]'=1/2·㏑(e∧-2x+xe∧-2x)
+1/2x·[1/(e∧-2x+xe∧-2x)]·(e∧-2x+xe∧-2x)'=1/2·㏑(e∧-2x+xe∧-2x)
+1/2x·[1/(e∧-2x+xe∧-2x)]·{-2e∧-2x+e∧-2x+x·(-2)
e∧-2x
}
∧ - степень
2 votes
Thanks 1
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Answers & Comments
Verified answer
1. = (-3arcsinx)'+(4√2x)'=-3/√(1-x²)+4·2/2√2x=-3/√(1-x²)+2√2/x2. =(1/6x⁶)'·(e∧6x+e∧-6x)+1/6x⁶·(e∧6x+e∧-6x)'=x⁵·(e∧6x+e∧-6x)+1/6x⁶·(6e∧6x
-6e∧-6x)=x⁵·(e∧6x+e∧-6x)+x⁶·(e∧6x-e∧-6x)
3. =(x/2)'·㏑(e∧-2x+xe∧-2x)+1/2x·[㏑(e∧-2x+xe∧-2x)]'=1/2·㏑(e∧-2x+xe∧-2x)
+1/2x·[1/(e∧-2x+xe∧-2x)]·(e∧-2x+xe∧-2x)'=1/2·㏑(e∧-2x+xe∧-2x)
+1/2x·[1/(e∧-2x+xe∧-2x)]·{-2e∧-2x+e∧-2x+x·(-2)e∧-2x}
∧ - степень