几道小题求解d(x^(1/2)),d(cosx),d(1/x),d(a^x)验证y=e^x(sinx)满足下面等式y′′-2y′+2y

Question

几道小题求解
d(x^(1/2)),d(cosx),d(1/x),d(a^x)
验证y=e^x(sinx)满足下面等式y′′-2y′+2y

Answer 1

d(x^(1/2))=(1/2)(x^(-1/2))dxd(cosx)=-sinxdxd(1/x)=-dx/x²d(a^x)=a^xlnadxy=e^x(sinx)y′=e^x(sinx+cosx)y''=e^x(sinx+cosx+cosx-sinx)=2cosxe^xy′′-2y′+2y =0