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Name: Class/Block: Date: Exploration: Product Rule Introduction In this exploration you will use the Exponents: Product Rule applet to explore properties of product of exponents. Step 1: Launch the
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How to fill out exploration product rule

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How to fill out the exploration product rule:

01
Begin by identifying the expression that needs to be differentiated using the exploration product rule. This rule is used when differentiating a product of two functions.
02
Write out the expression as the product of the two functions: f(x) * g(x). For example, if the expression is (3x^2 + 4x) * (2x + 1), then f(x) = 3x^2 + 4x and g(x) = 2x + 1.
03
Differentiate the first function, f(x), with respect to x. In our example, differentiate 3x^2 + 4x to obtain the derivative of f(x).
04
Differentiate the second function, g(x), with respect to x. In our example, differentiate 2x + 1 to obtain the derivative of g(x).
05
Apply the exploration product rule formula: (f'(x) * g(x)) + (f(x) * g'(x)). Substitute the derivatives obtained in step 3 and step 4 into the formula.
06
Simplify and combine the terms to obtain the final derivative of the product of the two functions.

Who needs the exploration product rule:

01
The exploration product rule is commonly used in calculus, specifically in the process of differentiation. It is important for students and professionals studying calculus or using calculus in their respective fields.
02
Mathematicians, engineers, physicists, economists, and other professionals who deal with mathematical modeling and analysis often need to differentiate complex expressions involving the multiplication of two functions. The exploration product rule provides a systematic method for finding the derivative in such cases.
03
Students learning calculus or preparing for exams in calculus should be familiar with the exploration product rule. It is an essential tool for solving problems involving differentiation and understanding the behavior of functions.
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The exploration product rule requires companies to report details of their exploration activities and products.
Any company or individual engaged in exploration activities is required to file the exploration product rule.
The exploration product rule can be filled out online through the designated platform provided by the regulatory authority.
The purpose of the exploration product rule is to ensure transparency and accountability in the exploration activities of companies.
Information such as the location of exploration activities, types of products being explored, and any environmental impact assessments must be reported on the exploration product rule.
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