求以下函数的导数
3个回答
4(1) y=(2x-1)²
y'=2(2x-1)(2x-1)'
=(4x-2)*2
=8x-4
(2) y=10^x+x^10+ln10
y'=10^x*ln10+10x^9+0
=10^xln10+10x^9
(3) y=x²√x-3/x+e^x-cscx
y=x^(5/2)-3/x+e^x-cscx
y'=5/2x^(3/2)-(-3/x²)+e^x-(-cscx*ctanx)
=5/2x^(3/2)+3/x²+e^x+cscx*ctanx
5(1) y=xlnx
y'=1*lnx+x*1/x
=lnx+1
(2) y=e^xsinx
y'=e^xsinx+e^xcosx
=e^x(sinx+cosx)
(3) y=(2x-3)(x+1)²
y'=2(x+1)+(2x-3)*2(x+1)*1
=2(x+1)(1+2x-3)
=2(x+1)(2(x-1))
=4(x²-1)
=4x²-4
6(1) y=cosx/x
y'=(-sinx*x-cosx*1)/x²
=-(xsinx+cosx)/x²
(2) y=(1+x²)/(1-x²)
y'=(2x(1-x²)-(1+x²)(-2x))/(1-x²)²
=2x(1-x²+1+x²)/(1-x²)²
=4x/(1-x²)²
(3) y=cosx/(1+sinx)
y'=(-sinx(1+sinx)-cosx*cosx)/(1+sinx)²
=(-sinx-sin²x-cos²x)/(1+sinx)²
=(-sinx-1)/(1+sinx)²
=-1/(1+sinx)
