Question

高数中 导数 求导

Answer 1

方法如下图所示，请作参考，祝学习愉快：

Answer 2

Answer 3

(1)
y= e^{ [cos(lnx/x)]^2 }
y'
=e^{ [cos(lnx/x)]^2 } . ([cos(lnx/x)]^2)'
=e^{ [cos(lnx/x)]^2 } . { 2cos(lnx/x) } . [ cos(lnx/x) ]'
=e^{ [cos(lnx/x)]^2 } . { 2cos(lnx/x) } . [ -sin(lnx/x) ] . [lnx/x]'
=e^{ [cos(lnx/x)]^2 } . { 2cos(lnx/x) } . [ -sin(lnx/x) ] . [ (1-lnx)/x^2 ]
=-2sin(lnx/x).cos(lnx/x). [ (1-lnx)/x^2 ] .e^{ [cos(lnx/x)]^2 }
(2)
y= { xsinx . [(1-e^x)/(1+x)]^(1/3) }^ (1/5)
lny=(1/5)lnx + (1/5)lnsinx + (1/15)ln(1-e^x) - (1/15)ln(1+x)
y'/y =(1/5)(1/x) + (1/5)cotx - (1/15)[e^x/(1-e^x)] - (1/15)[1/(1+x)]
y' = {(1/5)(1/x) + (1/5)cotx - (1/15)[e^x/(1-e^x)] - (1/15)[1/(1+x)] } .
{ xsinx . [(1-e^x)/(1+x)]^(1/3) }^ (1/5)