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If the function g is the inverse of f and the derivative of f is f'(x) = sin x, then what is g'(x)?

1. cosec{g(x)}
2. sin{g(x)}
3. 1/sin{g(x)}
4. cos{g(x)}

Correct answer: cosec{g(x)}

Solution

The derivative of the inverse function g can be found using the formula g'(x) = 1/f'(g(x)). Since f'(x) = sin x, we have g'(x) = 1/sin(g(x)), which simplifies to cosec(g(x)).

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