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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Mia 1 month 2021-08-11T14:56:53+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-11T14:58:00+00:00

    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)

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