设y=ln(x+ex2),求dy后面的ex2是e的x次方 x的2次方
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设y=ln(x+ex2),求dy后面的ex2是e的x次方 x的2次方
设y=ln(x+ex2),求dy
后面的ex2是e的x次方 x的2次方
设y=ln(x+ex2),求dy后面的ex2是e的x次方 x的2次方
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y=ln(x+e^x^2)
dy=(x+e^x^2)^(-1)*(1+2xe^x^2)
x^y就是x的y次方
1/X+2e
上面肯定错的- -!
e^y=x+ex^2
两边求导
得e^y.y'=1+2xe^x^2
y'=(1+2xe^x^2)/(x+ex^2)
dy=(1+2xe^x^2)/(x+ex^2).dx
y=ln[x+e^(x^2)]看作是由y=lnu,u=x+e^(x^2)复合而成,所以
dy=d(lnu)=1/u×du=1/(x+e^(x^2))×d(x+e^(x^2))=1/(x+e^(x^2))×(dx+d(e^(x^2)))
e^(x^2)看作是由e^v,v=x^2复合而成,所以
d(e^(x^2))=d(e^v)=e^vdv=e^(x^2)d(x^2)=e^(x...
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y=ln[x+e^(x^2)]看作是由y=lnu,u=x+e^(x^2)复合而成,所以
dy=d(lnu)=1/u×du=1/(x+e^(x^2))×d(x+e^(x^2))=1/(x+e^(x^2))×(dx+d(e^(x^2)))
e^(x^2)看作是由e^v,v=x^2复合而成,所以
d(e^(x^2))=d(e^v)=e^vdv=e^(x^2)d(x^2)=e^(x^2)×2x dx
所以,
dy
=1/(x+e^(x^2))×(dx+d(e^(x^2)))
=1/(x+e^(x^2))×(dx+2xe^(x^2)dx)
=1/(x+e^(x^2))×(1+2xe^(x^2))dx
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