Question

CONTINUITY AND DIFFERENT
If . and w are functions of x, then show that
2 uuw
d
(u. v. w) =
du
dy
dw
V. W + u.
w + u.
in two ways-first by repeated application of product rule, second by logarithmic
differentiation​

Answer 1

Answer:

Using Product rule, in which u and v are taken as one

dx

d(uvw)

=

dx

d(uv)

w+

dx

d(w)

uv

w.v.

dx

d(u)

+w.u.

dx

d(v)

+u.v.

dx

d(w)

Now using logarithmic,

y=uvw

taking log on both sides, we have

logy=logu+logv+logw

y

1

dx

dy

=

u

1

dx

du

+

v

1

dx

dv

+

w

1

dx

dw

∴

dx

dy

=y×(

u

1

dx

du

+

v

1

dx

dv

+

w

1

dx

dw

)

dx

dy

=w.v.

dx

d(u)

+w.u.

dx

d(v)

+u.v.

dx

d(w)