Question

tan(x²-1)/x³-1

一,求下列函数的微分dy
(1)y=ln√1-x³(ln 根号下一减x的三次方)
(2)y=ln tan x÷2(ln tan 二分之x)
(3)y=tan²(1+2x²)(为二次方）
（4）y=arc tan 1-x²除以1+x²
二,求下列方程所确定的隐函数y=f（x）的微分dy
y²=x+ arc cos y

Answer 1

一
(1)y=(1/2)ln(1-x^3)
dy=(1/2)[(-3x^2)/(1-x^3)]dx
=(-3x^2)/[2(1-x^3)] dx
(2) dy=[1/tan(x/2)][sec(x/2)]^2 (1/2) dx
=dx/sinx
(3) dy=2tan(1+2x^2)[sec(1+2x^2)]^2 4xdx
=8xtan(1+2x^2)[sec(1+2x^2)]^2 dx
(4) dy=1/[1+(1-x^2)^2/(1+x^2)^2]
[-2x(1+x^2)-2x(1-x^2)] dx /(1+x^2)^2
=(-2x)/(1+x^4) dx
二.
2yy'=1-y'/[(1-y^2)^(1/2)]
y'=(1-y^2)^(1/2)/[1+2y(1-y^2)^(1/2)]