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Let F (x) = e ^(x) , G (x) =e ^(-x) and ...

Let `F (x) = e ^(x) , G (x) =e ^(-x) and H (x) = G (F(x)),` where x is a real variable. Then `(dH)/(dx) at x =0` is

A

1

B

`-1`

C

`(-1)/(e)`

D

`-e`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dH)/(dx)=G.(f(x)f.(x),` putting x = 0
G.(f(0)) f.(0)`
G.(x) = -e^(-x) = e^(x)`, putting x = 0 f.(0) = 1 also, f(0) = 1
So G.(1)1 `rArr -e^(-1) rArr(-1)/(e )`
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