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 Rationalised 2023-24
 MATHEMATICS
130
(iii)
Let y = cos–1 (ex) Using chain rule, we have
dy
dx  =
2
2
1
(
)
1
(
)
1
x
x
x
x
d
e
dxe
e
e
−
−
⋅
=
−
−
(iv)
Let y = ecos x