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Let f, g and h are differentiable funct...

Let `f, g and h` are differentiable functions. If `f(0) = 1; g(0) = 2; h(0) = 3` and the derivatives of theirpair wise products at `x=0` are `(fg)'(0)=6;(g h)' (0) = 4 and (h f)' (0)=5` then compute the value of `(fgh)'(0)`.

A

2

B

4

C

8

D

16

Text Solution

Verified by Experts

The correct Answer is:
C
`y=fgh`
`(dy)/(dx)=f'gh+fg'h+fgh'`
`=(1)/(2)(2f'gh+2fg'h+2fgh')`
`=(1)/(2)(h(f'g+g'f)+g(f'h+fh')+f(g'h+gh'))`
`=(1)/(2)[h.(fg)'+g.(fh)'+f.(gh)']`
`therefore" "(fgh)'(0)=(1)/(2)[h(0)(fg)'(0)+g(0)(fh)'(0)+f(0)(gh)'(0)]`
`=(1)/(2)(3xx6+2xx5+1xx4)`
`=(1)/(2)(18+10+4)=(32)/(2)=16`
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