Product Rule

The product rule is a formula used to find the derivative of a product of two functions. If you have two functions, f(x) and g(x), the product rule states that the derivative of their product is given by:

f'(x) * g(x) + f(x) * g'(x)

Where f'(x) is the derivative of the function f(x) and g'(x) is the derivative of the function g(x).

Example:

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

f'(x) = 2x and g'(x) = 3

So, the derivative of the product f(x) * g(x) is:

2x * 3x + x^2 * 3 = 6x^2 + 3x^2 = 9x^2

Study Guide:

1. Understand the concept of derivatives and how they relate to functions.
2. Learn the product rule formula: f'(x) * g(x) + f(x) * g'(x).
3. Practice applying the product rule to various functions and functions.
4. Be familiar with finding the derivatives of basic functions such as polynomials, exponential functions, and trigonometric functions.
5. Work on problems that involve using the product rule in combination with other derivative rules.
6. Review and practice multiple examples to ensure a solid understanding of the product rule and its application.

Remember, the product rule is a fundamental concept in calculus and is used to find the derivative of the product of two functions. Understanding and mastering this rule is crucial for success in calculus and higher-level mathematics.

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