作业帮y=xe^x^2的三阶导数怎样求?
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y=xe^x^2的三阶导数怎样求?
y=xe^x^2的三阶导数怎样求?
y=xe^x^2的三阶导数怎样求?
如图所示.
y=xe^x^2
导数 e^x^2+2x^2e^x^2
二阶导数 2xe^x^2+4xe^x^2+2x*2x^2e^x^2=6xe^x^2+4x^3e^x^2
三阶导数 6e^x^2+12x^2e^x^2+12x^2e^x^2+8x^4e^x^2
=6e^x^2+24x^2e^x^2+8x^4e^x^2
y=xe^(x^2 )
y’=( xe^(x^2 ))’
y’=x’e^(x^2 )+x(e^(x^2 ))’=e^(x^2 )+xe^(x^2 )(x^2)’=e^(x^2 )+ 2x^2 e^(x^2 )
y’’=(e^(x^2 )+ 2x^2 e^(x^2 ))’=(e^(x^2 ))’+ (2x^2 e^(x^2 ))’
y’’=2xe^(x^2 )+ (2...
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y=xe^(x^2 )
y’=( xe^(x^2 ))’
y’=x’e^(x^2 )+x(e^(x^2 ))’=e^(x^2 )+xe^(x^2 )(x^2)’=e^(x^2 )+ 2x^2 e^(x^2 )
y’’=(e^(x^2 )+ 2x^2 e^(x^2 ))’=(e^(x^2 ))’+ (2x^2 e^(x^2 ))’
y’’=2xe^(x^2 )+ (2x^2)' e^(x^2 )+2x^2(e^(x^2 ))’
y’’=2xe^(x^2 )+ 2*2xe^(x^2 )+2x^2*2xe^(x^2 )=6xe^(x^2 )+4x^3 e^(x^2 )=e^(x^2 )(6x+4x^3)
y’’’=[e^(x^2 )(6x+4x^3)]’
y’’’=(e^(x^2 ))’ (6x+4x^3)+ (e^(x^2 ))(6x+4x^3)’
y’’’=2xe^(x^2 )(6x+4x^3)+e^(x^2 )(6+12x^2)
y’’’=12x^2 e^(x^2 )+8x^4 e^(x^2 )+6e^(x^2 )+12x^2 e^(x^2 )
y’’’=6e^(x^2 )+24x^2 e^(x^2 )+8x^4 e^(x^2 )
收起
y'=x'*e^(x²)+x*[e^(x²)]'
=e^(x²)+x*e^(x²)*(x²)'
=e^(x²)+x*e^(x²)*2x
=(1+2x²)e^(x²)