1. Derivative Functions

I need to find the derivative of this function algebraically: y = (x – 1)^3 + 2

K-L

2. Do you mean by using the definition?

Can you do this one $y = x^{2}$?

How about this one $y = x^{2} + 32$?

3. The question says:

Consider the graph of y= (x-1)^3 +2
Use your rules of differentiation to find the derivative y' algebraically.

I don't really understand it.

4. First, let’s write it as $y(x) = \left( {x - 1} \right)^3 + 2$.
Then we have, $\begin{array}{rcl}
\frac{{dy}}{{dx}} & = & \lim _{h \to 0} \frac{{y(x + h) - y(x)}}{h} \\
& = & \lim _{h \to 0} \frac{{\left[ {\left( {x + h - 1} \right)^3 + 2} \right] - \left[ {\left( {x - 1} \right)^3 + 2} \right]}}{h} \\
\end{array}$

Now you do the algebra.

5. Thanks, that's already helped quite a bit.
Though I think I'm doing something wrong when I expand it:

(x^3 + h^3 + 3xh + 3xh -1^3 +2) - (x^3 -1^3 +2)

6. You need a great deal of practice on simple algebra.