Question

derivar en 4 pasos f(x) =3x^2- 4x +6
y f(x)= x^2 -2​

Answer 1

Respuesta:

Explicación paso a paso:

$3x^{2}-4x+6\\\\f(x+h)-f(x)=3(x+h)^{2}-4(x+h)+6-(3x^{2}-4x+6)=3(x^{2}+2(x)(h)+h^{2})-4(x+h)+6-(3x^{2}-4x+6)=\\\\=3x^{2}+6hx+3h^{2}-4x-4h+6-3x^{2}+4x-6=\\\\=6hx+3h^{2}-4h\\\\f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to 0}\frac{6hx+3h^{2}-4h}{h}=\lim_{h\to 0} 6x+3h-4=\\\\=6x-4$

$f(x) =x^{2}-2\\\\f(x+h)-f(x)=2(x+h)^{2}-2-(2x^{2}-2)=2(x^{2}+2(x)(h)+h^{2})-2-(2x^{2}-2)=\\\\=2x^{2}+4xh+2h^{2}-2-2x^{2}+2=\\\\=4xh+2h^{2}\\\\f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to 0} \frac{4xh+2h^{2}}{h}=\\\\=\lim_{h\to 0}\,\,4x+2h=4x$