求导 (1)y=根号2x+sinx (2)y=sinx*Inx (3)y=x/x^2+1 (4)y =In(sinx)

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求导 (1)y=根号2x+sinx (2)y=sinx*Inx (3)y=x/x^2+1 (4)y =In(sinx)
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求导 (1)y=根号2x+sinx (2)y=sinx*Inx (3)y=x/x^2+1 (4)y =In(sinx)
求导 (1)y=根号2x+sinx (2)y=sinx*Inx (3)y=x/x^2+1 (4)y =In(sinx)

求导 (1)y=根号2x+sinx (2)y=sinx*Inx (3)y=x/x^2+1 (4)y =In(sinx)
(1)y=根号2x+sinx
y'=1/(2√2x)+cosx
(2)y'=cosxlnx+sinx/x
(3)y'=(x^2+1-2x^2)/(x^2+1)^2=(1-x^2)/(x^2+1)^2
(4)y'=cosx/sinx=cotx

1)y`=2+cosx
2) y`=cosx*lnx+sinx/x
3) y`=-1/x^2
4) y`=cosx/sinx=cotx

1、
y=√2*x+sinx
y'=√2+cosx
2、
y=sinx*lnx
y'=lnx*cosx+sinx*1/x
=(sinx+xlnxcosx)/x
3、
y=x/(x²+1)
y'=[(x²+1)-x*(2x)]/(x²+1)²
=(1-x²)/(1+x²)²
4、
y=ln(sinx)
y'=1/sinx*(sinx)'
=1/sinx*cosx
=cotx