Question

求解高等数学

Answer 1

(1)
y = √{(x-1)(x-2)/[(x-3)(x-4)] }
lny =(1/2)[ ln(x-1)+ln(x-2)-ln(x-3)-ln(x-4) ]
y'/y =(1/2)[ 1/(x-1)+1/(x-2)-1/(x-3)-1/(x-4) ]
y'=(1/2)[ 1/(x-1)+1/(x-2)-1/(x-3)-1/(x-4) ].√{(x-1)(x-2)/[(x-3)(x-4)] }
(2)
y=lnx + √x +2
y' =1/x + 1/(2√x)
(3)
y=xsinx
y'
=x(sinx)' + sinx . (x)'
=x(cosx) + sinx . (1)
=xcosx +sinx
(4)
y=arctan2x
y'
=[1/(1 +(2x)^2)] .(2x)'
=[1/(1 +(2x)^2)] .(2)
=2/(1+4x^2)