Question

What are the two ways to derive the function and how do I do it

Answer 1

Given the equation of the function:

$f(x)=2x^2(x^3-3)$

We will find the derivative of the function in two ways.

The first way is by using the product rule:

So, the derivative of the function will be as follows:

$\begin{gathered} f^{\prime}(x)=4x\cdot(x^3-3)+2x^2\cdot3x^2 \\ f^{\prime}(x)=4x^4-12x+6x^4 \\ f^{\prime}(x)=10x^4-12x \end{gathered}$

The second way by expanding the function then use the power rule to find the derivative as follows:

$\begin{gathered} f(x)=2x^5-6x^2 \\ \\ f^{\prime}(x)=2\cdot5x^4-6\cdot2x \\ f^{\prime}(x)=10x^4-12x \end{gathered}$