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Question
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If r(x) =f [g(x)] find r' (2).
Solution
r(x) =f[g(x)]
∴ r'(x) = `"d"/"dx"f["g"(x)]`
= `f'["g"(x)]."d"/"dx"["g"(x)]`
= `f'["g"(x)].["g"'(x)]`
∴ r'(2) = `f'["g"(2)]."g"'(2)`
= `f'(6)."g"'(2)` ...[∵ g(x) = 6, when x = 2]
= –4 x 4 ...[From the table]
= –16.
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