How do you find the first and second derivative of x^2-2x-3?

1 Answer
May 12, 2016

If f(x)=x^2-2x-3
color(white)("XXX")f'(x)=2x-2 and
color(white)("XXX")f''(x)=2

Explanation:

The first derivative:
f'(x)=(df(x))/(dx)=(dcolor(red)(x^2))/(dx)-(dcolor(blue)(2x))/(dx)-(dcolor(green)(3))/(dx)

color(white)("XXXXXXXXX")=color(red)(2x^1)-color(blue)(2x^0)-color(green)(0)

color(white)("XXXXXXXXX")=color(red)(2x)-color(blue)(2)

The second derivative
The second derivative is just the derivative of the first derivative.
f''(x)=(df'(x))/(dx) = (dcolor(red)(2x^1))/(dx)-(dcolor(blue)(2x^0))/(dx)

color(white)("XXXXXXXXXX")=color(red)(2x^0)-color(blue)(0)

color(white)("XXXXXXXXXX")=color(red)(2)