How do you find the derivative of f(x)=3x^2 ?

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Answer 1 · 2018-05-16T16:15:34

#f'(x)=3(2x^(2-1))=3(2x^1)=6x#

We know that,

#color(red)((1)f'(x)=lim_(t->x)(f(t)-f(x))/(t-x)...to#[ limit definition ]

#color(blue)((2)lim_(x->a)(x^n-a^n)/(x-a)=na^(n-1)#

#f(x)=3x^2 =>f(t)=3t^2#

Using #(1)# we get

#f'(x)=lim_(t->x)(f(t)-f(x))/(t-x)#

#=lim_(t->x)(3t^2-3x^2)/(t-x)#

#=3lim_(t->x)(t^2-x^2)/(t-x)...toApply(2)#

#=3xx2x^(2-1)#

#=3xx2x^1#

#=6x#

Answer 2 · 2018-05-16T16:30:09

#6x#

Using the power rule:

#d/dx(x^n)=xn^(n-1)#

Apply:

#d/dx(3x^2)#

#rArr 6x^1#

#rArr 6x#