Question

求下列导函数(1) y=x^2cosx(2) y=(e^x+1)/(e^x-1)(3) y=sin^3*2x(4) y=

Answer 1

(1)

y=x^2cosx

y'=2xcosx-x^2sinx

(2)

y=(e^x+1)/(e^x-1)

=(e^x-1+2)/(e^x-1)

=1+2/(e^x-1)

y'=2*(-1/(e^x-1)^2)*e^x

=-2e^x/(e^x-1)^2

(3)y=sin^3 2x

y'=3sin^2 2x *cos2x *2

=6sin^2 2x cos2x

(4)

y=ln(x+√(1+x^2)

y'=1/(x+√(1+x^2)) *(1+1/2√(1+x^2) *2x)

=1/(√(1+x^2)+x) *(1+x/√(1+x^2))

=(√(1+x^2)-x)/(√(1+x^2)+x)(√(1+x^2)-x) *(1+x/√(1+x^2))

=(√(1+x^2)-x)/(1+x^2-x^2)*(1+x/√(1+x^2))

=(√(1+x^2)-x)*(1+x/√(1+x^2))

=√(1+x^2)+x-x-x^2/√(1+x^2)

=√(1+x^2)-x^2/√(1+x^2)

=(1+x^2-x^2)/√(1+x^2)

=1/√(x^2+1)