# Find the first four terms of the Taylor Series: #f(x)=xe^x# given #a=0#?

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Why is Slader using 1st-4th differentials, to find the first four terms?

Why is Slader using 1st-4th differentials, to find the first four terms?

##### 2 Answers

#### Explanation:

So...

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First four non-zero terms:

#### Explanation:

The

For our case,

So, to find the first

As the **we're generally interested in non-zero terms** , we can take the fourth derivative and find the next term (this is, I presume, why the first four derivatives were taken, as you need four derivatives to get four non-zero terms with this function):

Alternatively, we can use known Taylor series, which is easier with this function: (this method requires no derivatives)

Evaluate from