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A table of values of f, g, f' and g' is given : If r(x) =f [g(x)] find r' (2). - Mathematics and Statistics

Sum

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).

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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.

Concept: Geometrical Meaning of Derivative
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