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}`