# Derivative

#### skweres1

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

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

#### sa-ri-ga-ma

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

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

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

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!!!