1)y'=(x+1)'e^x+(x+1)(e^x)'=e^x+(x+1)e^x=e^x(x+2)
2)y'=(x²)'e^(x²+3x)+x²(e^(x²+3x))'=2xe^(x²+3x)+x²e^(x²+3x)(2x+3)=xe^(x²+3x)(2x²+3x+2)
3)y'=[(x²=1)'e^x-(x²+1)(e^x)']/(e^x)²=[2xe^x-(x²+1)e^x]/e^2x=e^x(2x-x²-1)/e^2x=(2x-x²-1)/e^x
4)y'=x'2^(3x+x²)+x(2^(3x+x²))'=2^(3x+x²)+x2^(3x+x²)㏑2(3+2x)=2^(3x+x²)(1+x㏑2(3+2x))
5)y'=(3x+5x²+x³)'4^x²+(3x+5x²+x³)(4^x²)'=(3+10x+3x²)4^x²+(3x+5x²+x³)4^x²㏑4×2x=4^x²(3+10x+x²+2x㏑4(3x+5x²+x³))