it's asking on the slope of it for the f⁻¹(x), so you have to get the inverse firstly, then we can simply get the derivative by implicit differentiation,
[tex]\bf f(x)=4x^5-\cfrac{1}{x^4}\qquad \stackrel{inverse}{x=4y^5-\cfrac{1}{y^4}}\implies x=4y^5-y^{-4}
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\stackrel{\textit{implicit differentiation}}{1=4\left(5y^4\frac{dy}{dx} \right)-\left(-4y^{-5}\frac{dy}{dx} \right)}\implies 1=20y^4\cfrac{dy}{dx}+4y^{-5}\cfrac{dy}{dx}
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1=\cfrac{dy}{dx}(20y^4+4y^{-5})\implies \cfrac{1}{20y^4+4y^{-5}}=\cfrac{dy}{dx}
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\left. \cfrac{1}{20y^4+\frac{4}{y^5}}=\cfrac{dy}{dx} \right|_{3,1}\implies \cfrac{1}{20(1)^4+\frac{4}{(1)^5}}\implies \cfrac{1}{24}[/tex]
