If the function $f(x)=x^{3}+e^{\frac{x}{2}}$ and $g(x)=f^{-1}(x)$, then the value of $g'(1)$ is ______.

If the function f(x)=x³+e^(x/2) and g(x)=f⁻¹(x), then the value of g'(1) is ______. $f(x) = x^3 + e^{x/2}$ $g(x) = f^{-1}(x)$ $\text{To find: } g'(1)$ $g'(x) = \dfrac{1}{f'(g(x))}$ $f(g(1)) = 1, \quad f(0) = 0 + e^{0} = 1$ $\Rightarrow g(1) = 0$ $f'(x) = 3x^2 + \dfrac{1}{2}e^{x/2}$ $f'(0) = 0 + \dfrac{1}{2} = \dfrac{1}{2}$ $g'(1) = \dfrac{1}{f'(g(1))} = \dfrac{1}{f'(0)} = \dfrac{1}{1/2} = 2$ $\boxed{g'(1) = 2}$