What is the derivative of #x^2#?

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Answer 1 · 2018-05-23T15:11:29

#2x#

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

Answer 2 · 2018-05-23T19:10:00

#2x#

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!

Answer 3 · 2018-05-23T20:09:40

#2x#

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 #