最后一道y=lnsin（x-1/x),求y的导数吧就是y′x100打错了是lnsin（x-1/x)

Question

最后一道y=lnsin（x-1/x),求y的导数吧就是y′x
100
打错了是lnsin（x-1/x)

Answer 1

答：y=ln [sin(x-1/x)]y'(x)= {1/[sin(x-1/x) }*[sin(x-1/x)] '={1/[sin(x-1/x)] }*cos(x-1/x)*(x-1/x) '={1/[sin(x-1/x)] }*cos(x-1/x)*(1+1/x^2)=(x^2+1)*[cot (x-1/x)] / (x^2)