Question

Calcular la derivada de F(x)=4x^2-5x+3 con base en la definición F(x)=lim f(x+h) - f(x)/h x->0

Answer 1

$y=4 x^{2} -5x+3 \lim_{h \to \ 0} \frac{f(x+h)-f-(x)}{h} \lim_{h \to \ 0} \frac{4(x+h) ^{2}-5(x+h)+3-(4 x^{2} -5x+3) }{h} \lim_{h \to \ 0} \frac{4( x^{2} +2xh+ h^{2} )-5(x+h)+3-(4 x^{2} -5x+3) }{h} \lim_{h \to \ 0} \frac{4 x^{2} +8xh+4 h^{2}-5x-5h+3-4 x^{2} +5x-3 }{h} \lim_{h \to \ 0} \frac{8xh+4 h^{2}-5h }{h} \lim_{h \to \ 0} \frac{h(8x+4h-5)}{h} \lim_{h \to \ 0} 8x+4h-5 \lim_{h \to \ 0} 8x-5$