求这些数学导数问题的求解过程和答案。

(1) y=x^3+3^x-ln3

y'=3x^2+3^xln3

(2) y=arctan√x

y=1/[1+(√x)^2]×(√x)'

= 1/(1+x)×1/(2√x)

=1/[2√x(1+x)]

(3) y=lnsinx

y'=1/sinx×(sinx)'

=1/sinx×cosx

=cotx

④y=x^sinx(x & gt；0)

lny=sinxlnx

1/y×y ' = cosxlnx+sinx×1/x

y'=y(cosxlnx+1/xsinx)

=x^sinx(cosxlnx+1/xsinx)

2、y=lnsin^2(1/x)

dy=1/[sin^2(1/x)]×[sin^2(1/x)]'dx

=1/[sin^2(1/x)]×2sin(1/x)×[sin(1/x)]'dx

= 2/[sin(1/x)]×cos(1/x)×(1/x)' dx

=2cot(1/x)×(-1/x^2)dx

=-2cot(1/x)/x^2dx

3、ye^x+lny=1

y'e^x+ye^x+1/yy'=0

(e^x+1/y)y'=-ye^x

y'=-ye^x/(e^x+1/y)

=-y^2e^x/(ye^x+1)

即:dy/dx =-y 2e x/(ye x+1)