(1) f′(x)=−3(x+Δx)+4+3x−4Δx=−3f'(x) = \frac{-3(x+\Delta x)+4+3x-4}{\Delta x} = -3f′(x)=Δx−3(x+Δx)+4+3x−4=−3 (2) f′(x)=limΔx→0(x+Δx)2−2(x+Δx)−3−x2+2x+3Δx=limΔx→0x2+2xΔx+Δx2−2x−2Δx−3−x2+2x+3Δxf'(x) = \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2 - 2(x+\Delta x) - 3 - x^2 + 2x + 3}{\Delta x} = \lim_{\Delta x \to 0} \frac{x^2 + 2x\Delta x + \Delta x^2 - 2x - 2\Delta x - 3 - x^2 + 2x + 3}{\Delta x}f′(x)=limΔx→0Δx(x+Δx)2−2(x+Δx)−3−x2+2x+3=limΔx→0Δxx2+2xΔx+Δx2−2x−2Δx−3−x2+2x+3 =2x−2= 2x - 2=2x−2