Question

If f(0) = 3, f'(0) = 2, then`"d"/("d"x) { log "f"(sin x + 3x^2)}` at x  0 is ______.

Options

• `2/3`

• `3/2`

• 2

• 0

Answer 1

If f(0) = 3, f'(0) = 2, then`"d"/("d"x) { log "f"(sin x + 3x^2)}` at x  0 is `2/3`.

Explanation:

Let y = `"d"/("d"x) [log"f"(sinx + 3x^2)]`

= `1/("f"(sin x + 3x^2)) * "d"/("d"x)["f"(sinx + 3x^2)]`

= `1/("f"(sinx + 3x^2))*"f'"(sinx + 3x^2)* "d"/("d"x) (sinx + 3x^2)`

= `("f'"(sinx + 3x^2)(cosx + 6x))/("f"(sinx + 3x^2))`

∴ `(y)_((x = 0)) = ("f'"(0).1)/("f"(0)) = 2/3`