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leevina
@leevina
July 2022
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2.10.Производные, помогите пожалуйста
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Удачник66
Verified answer
1) y=x^2*e^(2-x)
y'=2x*e^(2-x)+x^2*e^(2-x)(-1)=
=e^(2-x)*(2x-x^2)
2) y=кор.куб(cos x)=(cos x)^(1/3)
y'=1/3*(cos x)^(-2/3)*(-sin x)=
=-sin x/(3(cos x)^(2/3))
3) y=(x^2-1)/(x^2+1)=1 - 2/(x^2+1)
y'=2*2x/(x^2+1)^2=4x/(x^2+1)^2
4) y=2^(1-x^2)
y'=2^(1-x^2)*(-2x)*ln 2
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Answers & Comments
Verified answer
1) y=x^2*e^(2-x)y'=2x*e^(2-x)+x^2*e^(2-x)(-1)=
=e^(2-x)*(2x-x^2)
2) y=кор.куб(cos x)=(cos x)^(1/3)
y'=1/3*(cos x)^(-2/3)*(-sin x)=
=-sin x/(3(cos x)^(2/3))
3) y=(x^2-1)/(x^2+1)=1 - 2/(x^2+1)
y'=2*2x/(x^2+1)^2=4x/(x^2+1)^2
4) y=2^(1-x^2)
y'=2^(1-x^2)*(-2x)*ln 2