Product Rule

The product rule is a basic rule in calculus that allows us to find the derivative of a product of two functions. It is given by the formula:

(f * g)' = f'g + fg'

Where f and g are differentiable functions and f' and g' are their respective derivatives.

Example:

Let's say we have two functions, f(x) = 3x^2 and g(x) = 2x + 1. To find the derivative of the product of these two functions, we can use the product rule:

(f * g)' = (3x^2)'(2x + 1) + (3x^2)(2x + 1)'

= 6x(2x + 1) + 3x^2(2)

= 12x^2 + 6x + 6x^2

= 18x^2 + 6x

So, the derivative of f(x) * g(x) is 18x^2 + 6x.

Study Guide:

To use the product rule, follow these steps:

1. Differentiate the first function and keep the second function as is.
2. Then, add the first function as is and differentiate the second function.
3. Finally, combine the results using the product rule formula.

Remember to practice using the product rule with different functions to become comfortable with the process.

Hope this helps!

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