Question

求以下函数的导数。谢谢

Answer 1

1. y'=nsin^(n-1)x cosnx-nsin^n x sin nx=nsin^(n-1)x (cos nx - sinx sin nx)

2. y'=2xcos√(1+x^2) / √(1+x^2)-cos[arccot √x]/x√x

3. y'=sec^2(a^x) a^x lna  +ax^(a-1)sec^2x^a / sec^2(arctanx^a)

4. tany=(x+1)/(x-1)    y'sec^2 y=-2/(x-1)^2    y'=-2/{(x-1)^2 sec^2 [arctan(x+1)/(x-1)]}

5. y'=-sin[arctane^(-x)] [arctane^(-x)]'=sin[arctane^(-x)] e^(-x)/sec^2arctane^(-x)]