# How do you differentiate #e^x(x^2-3)#?

##### 4 Answers

#### Explanation:

You need to use the product rule to differentiate this. The product rule states that:

So, put into product rule gives:

#### Explanation:

Use the rule for finding the derivative of the product of two functions.

Here,

Put 'em all together:

...Wolfram tells me I need to factor:

GOOD LUCK

Use the product rule:

#### Explanation:

I preface this by saying that this at the moment is a product rule question posted in the chain rule section. Thus, I must consider both the possibility that it was posted in the wrong section, and the possibility that it was written incorrectly. Answers for both possibilities are below, please choose the appropriate one.

**IF YOU MEANT #e^x*(x^2-3)#**

This as written is not a case of the chain rule, but rather of the product rule. The product rule states that given

Here we have

**If you had instead meant #e^(x^2-3)#, you would use the chain rule.**

The chain rule states that for a composition of functions

Here we would have

How about using the Multiplication Rule?

#### Explanation:

Which is, in general:

Here,

and

So we have:

which fits into the formula like this:

(it doesn't change when differentiated)

and

(The exponent comes down in front leaving

So,

Let's simplify:

We don't need those last parentheses:

Now we can factor out the

which simplifies even more to:

The quadratic if factorable:

Me, I'd leave it like this:

I don't know if your teacher would want: