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leevina
@leevina
August 2022
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2.2.Продифференцировать неявно заданную функцию
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100275
4xy^3+2xy^2+x^2-6xy+x=0
4(x'y^3+x(y^3)')+2(x'y^2+x(y^2)')+(x^2)'-6(x'y+xy')+x'=0
4(y^3+x*3y^2*y')+2(y^2+
x*2y*y')+2x-6(y+xy')+1=0
4y^3+4x*3y^2*y'+2y^2+2
x*2y*y'+2x-6y-xy'+1=0
4y^3+12xy^2*y'+2y^2+4xy*y'+2x-6y-xy'+1=0
12xy^2*y'+4xy*y'-xy'=-(4y^3+2y^2+2x-6y+
1)
(12xy^2+4xy-x)y'=-(4y^3+2y^2+2x-6y+1)
y'=-(4y^3+2y^2+2x-6y+1)/(12xy^2
+4xy-x)
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Answers & Comments
4(x'y^3+x(y^3)')+2(x'y^2+x(y^2)')+(x^2)'-6(x'y+xy')+x'=0
4(y^3+x*3y^2*y')+2(y^2+x*2y*y')+2x-6(y+xy')+1=0
4y^3+4x*3y^2*y'+2y^2+2x*2y*y'+2x-6y-xy'+1=0
4y^3+12xy^2*y'+2y^2+4xy*y'+2x-6y-xy'+1=0
12xy^2*y'+4xy*y'-xy'=-(4y^3+2y^2+2x-6y+1)
(12xy^2+4xy-x)y'=-(4y^3+2y^2+2x-6y+1)
y'=-(4y^3+2y^2+2x-6y+1)/(12xy^2+4xy-x)