几个高数题1.y=x^(e^x)+e^(e^x),求dy2.x=e^(2t)*(cost)^2,y=e^(2t)*(si
1个回答
1.dy=d(x^(e^x))+d(e^(e^x))
=x^(e^x)d(e^xlnx)+e^(e^x)d(e^x)
=x^(e^x)(lnx+1/x)e^xdx+e^(e^x)e^xdx
=[x^(e^x)(lnx+1/x)+e^(e^x)]e^xdx
2.∵dx=e^(2t)d(cos²t)+cos²td(e^(2t))
=-e^(2t)sin(2t)dt+2e^(2t)cos²tdt
=[cos²t-sin(2t)]e^(2t)dt
dy=e^(2t)d(sin²t)+sin²td(e^(2t))
=e^(2t)sin(2t)dt+2e^(2t)sin²tdt
=[sin²t+sin(2t)]e^(2t)dt
∴dy/dx=[sin²t+sin(2t)]/[cos²t-sin(2t)]
3.y'=[(x²-x+1)^x ]'
=(x²-x+1)^x*[xln(x²-x+1)]'
=(x²-x+1)^x*[ln(x²-x+1)+x(2x-1)/(x²-x+1)]
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