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Let and let be the inverse function of . Notice that .
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Q. Let and let be the inverse function of . Notice that .
- Use Inverse Function Derivative Formula: To find , we need to use the formula for the derivative of the inverse function:
- Find Derivative of : First, we need to find which is the derivative of ..
- Calculate h'(\-1): Since h(\-1) = 10, we need to find h'(\-1) to use in our formula.$h'((-1\)) = (-1\) - \(10\)((-1\))^{\(4\)} = (-1\) - \(10\)(\(1\)) = (-1\) - \(10\) = (-11\).
- Find \(f'(10)\): Now we can find \(f'(10)\) using the formula.\(\newline\)\(f'(10) = \frac{1}{h'(f(10))} = \frac{1}{h'(-1)} = \frac{1}{-11}.\)
- Final Result: So, \(f^{\prime}(10) = -\frac{1}{11}.\)
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