1.所求面積=∫(0,1)(2x-x)dx+∫(1,2)(2x-x²)dx
=(x²/2)│(0,1)+(x²-x³/3)│(1,2)
=1/2+4-8/3-1+1/3
=7/6
2.∵z=y^x=e^(xlny)
∴z關(guān)于x的偏導(dǎo)數(shù)δz/δx=δ[e^(xlny)]/δx
=e^(xlny)*lny
=y^x*lny
z關(guān)于y的偏導(dǎo)數(shù)δz/δy=δ[e^(xlny)]/δy
=e^(xlny)*(x/y)
=y^x*x/y
=x*y^(x-1)