Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1.
| x |
f(x) |
g(x) |
f'(x) |
g'(x) |
| 0 |
1 |
1 |
5 |
1/3 |
| 1 |
3 |
-4 |
- 1/3 |
- 8/3 |
(i) The derivative of f[g(x)] w.r.t. x at x = 0 is ____
(ii) The derivative of g[f(x)] w.r.t. x at x = 0 is ____
(iii) The value of \(\left[\frac{d}{dx}[x^{10} + f(x)]^{-2}\right]_{x = 1}\) is _____
(iv) The derivative of f[(x + g(x))] w.r.t. x at x = 0 is _____
