Найти производную y=√x^2+1/x Y=(cos3x+6)^2 Y=(x^3-4x^2)^16. Created by Akbotta. algebra-ru

x Y=(cos3x+6)^2 Y=(x^3-4x^2)^16...

Akbotta @Akbotta

July 2022 1 6 Report

Найти производную y=√x^2+1/x
Y=(cos3x+6)^2
Y=(x^3-4x^2)^16

Answers & Comments

mikael2

Verified answer

y'=(u/v)'=1/v²[u'v-v'u] u=√(x²+1) u'=1/2√(x²+1)
v=x v'=1
y'=1/x²[x/√(x²+1)-√(x²+1)]
-----------------------------------
y'=2(cos3x+6)*(-sin3x)*3
--------------------------------------
y'=16(x³-4x²)^15*(3x²-8x)

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Answers & Comments

Verified answer

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