Question

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 ______.

पर्याय

• 1

• - 1

• -`1/"e"`

• - e

Answer 1

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 -`underline(1/"e")`.

Explanation:

H(x) = G[F(x)]

`= "e"^(-"e"^x)`

∴ H'(x) = `- "e"^x * "e"^(-"e"^x)`

∴ H'(0) = `- "e"^0 * "e"^(-"e"^0)`

`= - "e"^-1`

`= - 1/"e"`