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    • https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.15%3A_Derivatives
      We start by calculating Δf: Δf=f(x+Δx)f(x)=(x+Δx)2x2=x2+2xΔx+Δx2x2=2xΔx+Δx2 We now calcu...We start by calculating Δf: Δf=f(x+Δx)f(x)=(x+Δx)2x2=x2+2xΔx+Δx2x2=2xΔx+Δx2 We now calculate ΔfΔx: ΔfΔx=2xΔx+Δx2Δx=2x+Δx and take the limit Δx0: \[\begin{aligned} \frac{df}{dx}&=\lim_{\Delta x\to 0 }\frac{\Delta f}{\Delta x}\\ &=\lim_{\Delta x\to 0 }(2x+\…

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