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Whithoutme
@Whithoutme
August 2022
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найти все значения x, при каждом из которых производная функции: y(x)=3x^3*lnx-81xlnx-10x^3+324x
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ShirokovP
Verified answer
Y ' (x) = (
3x^3*lnx-81xlnx-10x^3+324x
)' =
= (3x^3)'*lnx + (lnx)'*3x^3 - ((81x)'*lnx + (lnx)'*81x) - 10*3x^2 + 324 =
= 9x^2 lnx + 3x^2 - 81lnx - 81 - 30x^2 + 324 =
= 9(x - 3)(x + 3) (lnx - 3) = 0
x - 3 = 0
x = 3
x + 3 = 0
x = - 3
lnx = 3
x = e^3
Ответ
- 3; 3; e^3
2 votes
Thanks 1
sedinalana
Y`=9x²*lnx+3x³/x-81lnx-81x/x-30x²+324=0
9x²*lnx+3x²-81lnx-81-30x²+324=0
9x²*lnx-81lnx-27x²+243=0
9lnx*(x²-9)-27*(x²-9)=0
(x²-9)(9lnx-27)=0
9(x-3)(x+3)(lnx-3)=0
x-3=0⇒x=3
x+3=0⇒x=-3
lnx=3⇒x=e^3
1 votes
Thanks 0
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Answers & Comments
Verified answer
Y ' (x) = ( 3x^3*lnx-81xlnx-10x^3+324x )' == (3x^3)'*lnx + (lnx)'*3x^3 - ((81x)'*lnx + (lnx)'*81x) - 10*3x^2 + 324 =
= 9x^2 lnx + 3x^2 - 81lnx - 81 - 30x^2 + 324 =
= 9(x - 3)(x + 3) (lnx - 3) = 0
x - 3 = 0
x = 3
x + 3 = 0
x = - 3
lnx = 3
x = e^3
Ответ
- 3; 3; e^3
9x²*lnx+3x²-81lnx-81-30x²+324=0
9x²*lnx-81lnx-27x²+243=0
9lnx*(x²-9)-27*(x²-9)=0
(x²-9)(9lnx-27)=0
9(x-3)(x+3)(lnx-3)=0
x-3=0⇒x=3
x+3=0⇒x=-3
lnx=3⇒x=e^3