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![\displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}{h}\\\lim_{h\to0}\frac{[4(x+h)^2-3(x+h)]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{[4(x^2+2xh+h^2)-3x-3h]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{[4x^2+8xh+4h^2-3x-3h]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{4x^2+8xh+4h^2-3x-3h-4x^2+3x}{h}\\\lim_{h\to0}\frac{8xh+4h^2-3h}{h}\\\lim_{h\to0}\frac{h(8x+4h-3)}{h}\\\lim_{h\to0}8x+4h-3\\\\8x+4(0)-3\\8x+0-3\\\boxed{\boxed{8x-3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%5B4%28x%2Bh%29%5E2-3%28x%2Bh%29%5D-%5B4x%5E2-3x%5D%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%5B4%28x%5E2%2B2xh%2Bh%5E2%29-3x-3h%5D-%5B4x%5E2-3x%5D%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B%5B4x%5E2%2B8xh%2B4h%5E2-3x-3h%5D-%5B4x%5E2-3x%5D%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B4x%5E2%2B8xh%2B4h%5E2-3x-3h-4x%5E2%2B3x%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7B8xh%2B4h%5E2-3h%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D%5Cfrac%7Bh%288x%2B4h-3%29%7D%7Bh%7D%5C%5C%5Clim_%7Bh%5Cto0%7D8x%2B4h-3%5C%5C%5C%5C8x%2B4%280%29-3%5C%5C8x%2B0-3%5C%5C%5Cboxed%7B%5Cboxed%7B8x-3%7D%7D "\displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}{h}\\\lim_{h\to0}\frac{[4(x+h)^2-3(x+h)]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{[4(x^2+2xh+h^2)-3x-3h]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{[4x^2+8xh+4h^2-3x-3h]-[4x^2-3x]}{h}\\\lim_{h\to0}\frac{4x^2+8xh+4h^2-3x-3h-4x^2+3x}{h}\\\lim_{h\to0}\frac{8xh+4h^2-3h}{h}\\\lim_{h\to0}\frac{h(8x+4h-3)}{h}\\\lim_{h\to0}8x+4h-3\\\\8x+4(0)-3\\8x+0-3\\\boxed{\boxed{8x-3}}")
