I need to find the derivative of this function algebraically: y = (x – 1)^3 + 2
Please help!
Thank-you in advance,
K-L
First, let’s write it as $\displaystyle y(x) = \left( {x - 1} \right)^3 + 2$.
Then we have, $\displaystyle \begin{array}{rcl}
\frac{{dy}}{{dx}} & = & \lim _{h \to 0} \frac{{y(x + h) - y(x)}}{h} \\
& = & \lim _{h \to 0} \frac{{\left[ {\left( {x + h - 1} \right)^3 + 2} \right] - \left[ {\left( {x - 1} \right)^3 + 2} \right]}}{h} \\
\end{array}$
Now you do the algebra.