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

2 Answers
May 16, 2018

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

Explanation:

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

May 16, 2018

6x

Explanation:

Using the power rule:

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

Apply:

d/dx(3x^2)

rArr 6x^1

rArr 6x