导数习题(1)y=(3+2^3)√1+4x^2(2)y=ln³√x+³√lnx(3)y=ln1+√x/1-√x(4)y=(sinnx)(cos^nx)(5)y=lntanx/2(6)y=x^2cot1/x

Question

导数习题
(1) y=(3+2^3)√1+4x^2
(2) y=ln³√x +³√lnx
(3) y=ln 1+√ x / 1-√ x
(4) y=(sin nx)(cos^n x)
(5) y=ln tan x/2
(6) y=x^2 cot 1/x

Answer 1

导数习题
(1) y=(3+2³)√(1+4x²)=11√(1+4x²)
y'=88x/[2√(1+4x²)]=44x/√(1+4x²)；
(2) y=ln³√x +³√lnx
y=(1/3)lnx+(lnx)^(1/3)
y'=1/(3x)+(1/3)[(lnx)^(-2/3)]/x=1/(3x)+1/[3x(lnx)^(2/3)]
(3) y=ln(1+√ x)/(1-√ x)
定义域：x≧0且(1+√ x)/(1-√ x)>0,故得定义域为0≦x