Difficult
Let $f$ and $g$ be differentiable functions on $R$ such that $f \circ g$ is the identity function. If for some $a, b \in R$,$g^{\prime}(a) = 5$ and $g(a) = b$,then $f^{\prime}(b)$ is equal to
- A$2/5$
- B$1$
- C$1/5$
- D$5$
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View SolutionMatch the functions in List-$I$ with their derivatives given in List-$II$.
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| List-$I$ | List-$II$ |
| $A$. $\sec^{-1} x$ | $I$. $\frac{1}{1-x^2}, x \in (-1, 1)$ |
| $B$. $\tanh^{-1} x$ | $II$. $\frac{-1}{|x| \sqrt{x^2+1}}, x \neq 0$ |
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