Home
Class 12
MATHS
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`
Promotional Banner

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

Similar Questions

Explore conceptually related problems

Let f,g: (a,b) to R be differentiable functions show that d ((f)/(g)) = (gf' dx - fg'dx)/(g ^(2)) (where g ne 0)

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then,

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let x = f(t) and y = g(t), where x and y are twice differentiable function If f^(')(0) = g^(')(0) = f^('')(0) = 2, g^(")(0) = 6 , then the value of ((d^(2)y)/(dx^(2))_(t=0) is equal to

Let f: (-5,5) rarr R be a differentiable function with f(4) = 1, f^(')(4) = 1, f(0) = -1 and f^(')(0) = 1 , If g(x) = f(2f^(2)(x)+2))^(2) , then - g^(')(0) equals

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n dg(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0fora l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d)none of these

Let f and g be function continuous in [a,b] and differentiable on [a,b] .If f(a)=f(b)=0 then show that there is a point c in (a,b) such that g'(c) f(c)+f'(c)=0 .