Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g^′( a )=5 and g( a )= b, then f^′( b ) is…

Let $\displaystyle f$ and $\displaystyle g$ be differentiable functions on $\displaystyle \mathbf{R}$ such that fog is the identity function. If for some $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbf{R}, g^{\prime}(\mathrm{a})=5$ and $\displaystyle g(\mathrm{a})=\mathrm{b}$, then $\displaystyle f^{\prime}(\mathrm{b})$ is equal to :