What is the derivative of #x^2#?

3 Answers
May 23, 2018

#2x#

Explanation:

Use that #(x^n)'=nx^(n-1)#

May 23, 2018

#2x#

Explanation:

Anytime we see a polynomial, we can use the Power Rule (see below) to find its derivative.

With the Power Rule, the exponent comes out front of the variable, and the power gets decremented by #1#. Doing this, we get

#2x^1#, or

#2x#

Hope this helps!

May 23, 2018

#2x#

Explanation:

By first principles:

#lim_( h to 0) (f(x+h) - f(x) )/ h = (dy)/(dx) #

#=> lim_(h to 0)( (x+h)^2 - x^2 )/ h #

#=> lim_(h to 0) ( x^2 +2xh + h^2 - x^2)/ h #

#=> lim_(h to 0) ( 2xh + h^2 )/ h #

#=> lim_(h to 0) 2x + h #

# = 2x #