Question

como resuelvo derivada de la funcion cuadrática el limite porfavor f(x) = 3x²+2x paso a paso​

Answer 1

$\mathsl{f(x)=3x^2+2x} \\\\ f'(x)= \lim_{h \to 0}\dfrac{f(x+h)-f(x)}{h} \\\\ \displaystyle{f'(x)= \lim_{h \to 0}\dfrac{[3(x+h)^2+2(x+h)]-[3x^2+2x]}{h}} \\\\\\f'(x)= \lim_{h \to 0}\dfrac{[3x^2+h^2+6xh+2x+2h]-3x^2-2x}{h} \\\\\\f'(x)= \lim_{h \to 0}\dfrac{h^2+6xh+2h}{h} \\\\\\f'(x)= \lim_{h \to 0}{h+6x+2}\\\\\\f'(x)= 0+6x+2\\\\\\f'(x)= 6x+2$