Question

求教这几道高数题答案

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Answer 1

解：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)]