The Product Rule for Finding Derivatives: Step-by-Step Explanation and Mathematical Notation

d/dx [uv]

To find the derivative of the product of two functions, u and v, denoted by uv, we can use the product rule

To find the derivative of the product of two functions, u and v, denoted by uv, we can use the product rule. The product rule states that the derivative of the product of two functions is equal to the derivative of the first function multiplied by the second function, plus the first function multiplied by the derivative of the second function.

In mathematical notation, if y = uv, then the derivative d/dx [uv] is given by:

d/dx [uv] = u * d/dx[v] + v * d/dx[u]

Let’s break this down step by step:

1. Differentiate the first function, u, with respect to x to find d/dx[u].
2. Differentiate the second function, v, with respect to x to find d/dx[v].
3. Multiply the first function, u, by the derivative of the second function, d/dx[v].
4. Multiply the second function, v, by the derivative of the first function, d/dx[u].
5. Add the two products obtained in steps 3 and 4 together.

So, d/dx [uv] = u * d/dx[v] + v * d/dx[u]

Note: Make sure to use proper notation and follow the rules of differentiation for each function when finding their derivatives.

More Answers:

Calculating the Derivative Using the Formal Definition: Understanding the Rate of Change and Tangent Line Slope
Understanding the Derivative of a Function: The Mathematics Behind Rate of Change
Understanding Continuity in Mathematics: Definition and Conditions

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