APFIVE Derivative of an Inverse Function
Let $$f(x)=\sqrt{1+x^2}$$ be an invertible function. Find the derivative of its inverse, $$g(y)= f^{-1}(y)$$, at the point where $$y=\sqrt{2}$$.
| x | f(x)=\sqrt{1+x^2} |
|---|---|
| 0 | 1 |
| 1 | \(\sqrt{2}\) |
| 2 | \(\sqrt{5}\) |
A
$$1+\sqrt{2}$$
B
$$2$$
C
$$\sqrt{2}$$
D
$$\frac{1}{\sqrt{2}}$$
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