${f}(x) = {g}(x) ^ {{h}(x)}$

$ {f}'(x) = \lim\limits_{\Delta{x} \to 0}\frac{{f}(x + \Delta{x}) - {f}(x)}{\Delta{x}}\\ = \lim\limits_{\Delta{x} \to 0}\frac{{g}(x + \Delta{x}) ^ {{h}(x + \Delta{x})} - {g}(x) ^ {{h}(x)}}{\Delta{x}}\\ = \lim\limits_{\Delta{x} \to 0}\frac{{g}(x + \Delta{x}) ^ {{h}(x + \Delta{x})} - {g}(x + \Delta{x}) ^ {{h}(x)} + {g}(x + \Delta{x}) ^ {{h}(x)} - {g}(x) ^ {{h}(x)}}{\Delta{x}}\\ = {g}(x) ^ {{h}(x)} (\frac{{g}'(x) {h}(x)}{{g}(x)} + {h}'(x)\ln {g}(x)) $