(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)
Es decir: dy / dx =-y 2e x/(ye x+1)