# What is the derivative of #f(x) = (2x - 3)^4 (x^2 + x + 1)^5#?

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#### Explanation

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Looking at the equation,

we first notice a couple patterns.

1. The function is a **product** of two terms

2. Each of the terms is a term with an **exponent** .

Since the function is a product of two terms, we know that we have to use the Product Rule to find the first derivative. The Product Rule states,

For an equation,

In our case,

where,

Now we need to calculate g'(x) and h'(x) for the product rule. For this, we need the Chain Rule. It states,

If

so, in our specific case,

Therefore,

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