Question

y=(x乘以根号x+3)e^2x ,y=x^x^2+e^x^2+x^e^x+e^e^x ,的导数是多少

Answer 1

y=(x√x+3)e^x

=(x^(3/2)+3)*e^x

y'=(3/2)x^(1/2)e^x+(x^(3/2)+3)e^x

y=x^(x^2)+e^x^2+x^(e^x)+e^(e^x)

y1=x^(x^2) lny1=x^2lnx y1'/y1=2xlnx+x y1'=(2xlnx+x)*x^(x^2)

y2=e^(x^2) lny2=x^2 y2'/y2=2x y2'=2xe^(x^2)

y3=x^(e^x) lny3=e^xlnx y3'/y3=e^xlnx+e^x/x y3'=(e^xlnx+e^x/x)*x^(e^x)

y4=e^(e^x) lny4=e^x y4'/y4=e^x y4'=e^x*e^(e^x)

y'= (2xlnx+x)*x^(x^2) + 2xe^(x^2) + (e^xlnx+e^x/x)*x^(e^x) +e^x*(e^(e^x))