How do you find the derivative of f(x)=1-x^2f(x)=1x2 using the limit process?

1 Answer
Feb 3, 2017

d/(dx) (1-x^2) = -2xddx(1x2)=2x

Explanation:

By definition the derivative is:

f'(x) = lim_(h->0) (f(x+h)-f(x))/h

Evaluate the limit in the case: f(x) = 1-x^2:

d/(dx) (1-x^2) = lim_(h->0) ((1-(x+h)^2-(1-x^2))/h)

:.d/(dx) (1-x^2) = lim_(h->0) (cancel(1)-cancel(x^2)-2hx-h^2cancel(-1)+cancel(x^2))/h

:.d/(dx) (1-x^2) = lim_(h->0) (-2hx-h^2)/h = lim_(h->0) (cancel(h)(-2x-h))/cancel(h)

:.d/(dx) (1-x^2) = lim_(h->0) (-2x-h) = -2x