设函数y=x^x+ln(arctan5x),求其导数dy/dx、微分dy
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设函数y=x^x+ln(arctan5x),求其导数dy/dx、微分dy
![设函数y=x^x+ln(arctan5x),求其导数dy/dx、微分dy](/uploads/image/z/54260-44-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0y%3Dx%5Ex%2Bln%28arctan5x%29%2C%E6%B1%82%E5%85%B6%E5%AF%BC%E6%95%B0dy%2Fdx%E3%80%81%E5%BE%AE%E5%88%86dy)
y'=(x^x)'+(ln(arctan5x)'
设f(x)=x^x
lnf(x)=xlnx
1/f(x)f'(x)=lnx+1
f'(x)=f(x)(lnx+1)=x^x(lnx+1)
ln(arctan5x)'=1/(arctan5x) * (1/(1+25x^2))*5=5/[(1+25x^2)(arctan5x)]
dy/dx=x^x(lnx+1)+5/[(1+25x^2)(arctan5x)]
dy={x^x(lnx+1)+5/[(1+25x^2)(arctan5x)]}dx
设f(x)=x^x
lnf(x)=xlnx
1/f(x)f'(x)=lnx+1
f'(x)=f(x)(lnx+1)=x^x(lnx+1)
ln(arctan5x)'=1/(arctan5x) * (1/(1+25x^2))*5=5/[(1+25x^2)(arctan5x)]
dy/dx=x^x(lnx+1)+5/[(1+25x^2)(arctan5x)]
dy={x^x(lnx+1)+5/[(1+25x^2)(arctan5x)]}dx
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