## CONTINUITY AND DIFFERENT If . and w are functions of x, then show that 2 uuw d (u. v. w) = du dy dw

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

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Math
10 months
2021-08-11T14:56:53+00:00
2021-08-11T14:56:53+00:00 1 Answer
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## Answers ( )

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)