t x:
(i)
e–x
(ii)   sin (log x), x > 0
    (iii)   cos–1 (ex)
 (iv)    ecos x
Solution
(i)
Let y = e– x Using chain rule, we have
dy
dx  =
x
d
e
dx
− ⋅
 (– x) = – e– x
(ii)
Let y = sin (log x) Using chain rule, we have
dy
dx  =
cos (log )
cos (log )
d(log )
x
x
x
dx
x
⋅
=
* Please see supplementary material on Page 222