《高等数学》课程教学资源（单元测试解答）第二章 导数与微分 习题三 复合函数求导

复合函数求导 1.y=simn5x,则x= C A.cos5x C B.5cos5x C C.5sin 5x C D.-cos5x 2.(e,= C A.'x) C B.e(s) C C.e)+(x) C D.e()-'(x) 3.y=In(In(lx》,则y= 1 1 C A.2xInvx(Invx) C B. 2xlnvx In(In/x) 1 1 C C.xInvxIn(In/x) C D.2xlnxin(in) 4.若y=f(ee/,则y'= C A.erf'e")e" C B.e(e")'(x) c C.erLf'(e")e*+f(e")f(x)] D.f'(e*e*+f(e)f"'(x) 5.y=arcsin x+tan,y= 2 C A.(arcsinx B.(arcm V1-x2 x9e2马 12

复合函数求导 1. ，则 _____________ ． A. B. C. D. 2． ( ) ( ) (e ) x x    ＝_______________． A.e ( ) ( ) x x    B. ( ) e  x C.e ( ) ( ) x x     D.e ( ) ( ) x x     3． y ln(ln(ln x))， 则 y  _____________． A. 2 ln (ln ) 1 x x x B. 2 ln ln(ln ) 1 x x x C. ln ln(ln ) 1 x x x D. 1 2xln xln(ln x) 4．若 y  f (e x )e f ( x) ,则y＝________________． A. f x x x e f (e )e ( )  B.e (e ) ( ) ( ) f x f x x  C.e [ (e )e (e ) ( )] ( ) f f f x f x x x x    D. f (e )e f (e ) f (x) x x x    5． ,则 _____________． A. B. C. D

1.A.解y=sin5x,由复合函数求导法，则%x=cos5x· 2.B.解若(e,由复合函数求导法，则(ea,=e,而不是 ep'(x),其为(ey=eo'(x). 3.B.解 y=1111 ln(lnN)'lnV√F2√F2 xInvxIn(Inv) 4.C.y'=f'(e*)e'e()+f(e)e.f'(x) =eLf(e*)e*+f(e*)f'(x)] 5B解y-cmr+经+oc()

1. A. 解 y  sin 5x，由复合函数求导法，则 y5  x  cos5x . 2. B. 解 若 ( ) ( ) (e ) x x    ，由复合函数求导法，则 ( ) ( ) (e ) x x    = ( ) e  x ，而不是 e ( ) ( ) x x    ，其为 x  x (e ) ( ) e ( ) ( ) x x    . 3.B. 解 . 2 ln ln(ln ) 1 2 1 1 ln 1 . ln(ln ) 1 x x x x x x x y     4. C. 解 (e )e e (e )e ( ) ( ) ( ) y f f f x x x f x x f x       =e [ (e )e (e ) ( )] ( ) f f f x f x x x x    5.B. 解               2 2 2 1 1 sec 1 1 2 arcsin 2 1 x x x x y x = ). 1 sec 2 1 (arcsin 2 1 2 2 2 x x x x x   