根号（10t）的导数是多少?还有f（x）=xsinx+cosx,则f`(π/2)的值为?

题目

根号（10t）的导数是多少?还有f（x）=xsinx+cosx,则f`(π/2)的值为?

答案

(√10 t )' = ((10 t )^(1/2))' = (1/2) ((10 t )^(-1/2)) (10 t )' = 5 (10 t )^(-1/2) 先求 f'(x) = sinx + x cosx - sinx = x cosx 再求 f'(π/2) = x cosx = π/2 (0) = 0