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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