# Derivative

#### skweres1

Calculate the derivative of the following function at the given points:

F(x)= 3x^2 xo=2

I am struggling with setting the problem up. Can someone please help me?? Thanks!!!

#### sa-ri-ga-ma

Calculate the derivative of the following function at the given points:

F(x)= 3x^2 xo=2

I am struggling with setting the problem up. Can someone please help me?? Thanks!!!
What is the derivative of x^2 with respect to x?

#### Chris L T521

MHF Hall of Fame
Calculate the derivative of the following function at the given points:

F(x)= 3x^2 xo=2

I am struggling with setting the problem up. Can someone please help me?? Thanks!!!
Are you allowed to use the short cut formulas or the limit definition?

If you can use the short cuts, apply the rule $$\displaystyle \frac{d}{dx}\left[x^n\right]=nx^{n-1}$$ when finding $$\displaystyle f^{\prime}(x)$$. Then evaluate at $$\displaystyle x_0=2$$

If you are supposed to use the limit definition, then evaluate $$\displaystyle \lim_{h\to0}\frac{f(2+h)-f(2)}{h}=\lim_{h\to0}\frac{3(2+h)^2-3(2)^2}{h}$$.

Does this make sense? Can you finish the problem?

skweres1

#### BobBali

The derivative of $$\displaystyle F(x) = 3x^ \(\displaystyle F(x)' = 6x$$

to find the derivative given an x-coordinate, say $$\displaystyle x=2$$
simply substitute x into the derived function above

$$\displaystyle F(2) = 6*2 = 12$$\)

skweres1

Yes THANK YOU!!!