Question

数学求导数

Answer 1

(1)
原式=2^x+2*[x^(1/2)]+[x^(-1/3)]
所以，y'=(2^x)*ln2+2*(1/2)*[x^(-1/2)]+(-1/3)*[x^(-4/3)]
=(2^x)*ln2+[x^(-1/2)]-(1/3)*[x^(-4/3)]

(3)
y'=(e^x)'*(sinx+cosx)+(e^x)*(sinx+cosx)'
=(e^x)*(sinx+cosx)+(e^x)*(cosx-sinx)
=2cosx*(e^x)

(5)y=(x-1)/(x+1)=[(x+1)-2]/(x-1)=1-[2/(x-1)]=1-2*[(x-1)^(-1)]
所以，y'=-2*(-1)*[(x-1)^(-2)]*(x-1)'
=2/(x-1)^2

(7)原式=x^2+x^(-5/2)+x^(-3)
所以，y'=2x-(5/2)*x^(-7/2)-3*x^(-4)