Find f '(x) and f ''(x).
f(x) = (x3 + 1)ex

and

Step-by-step explanation:

From the question,

f(x) = (x3 + 1)ex

That is,

Then , we can write that

To find f'(x), we will differentiate and then add it to the differential of

First, we will differentiate ,

Let (This is a product)

Then,

Hence,

Given , Using the product rule

Hence,

and

∴

For f ''(x)

To find f ''(x), will differentiate f '(x)

This is also a product, then we will apply the product rule

From the product rule,

Given , Using the product rule

Here, Let and

Then,

∴

Hence,

and