Product Rule For Derivatives | Summary and Q&A

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February 25, 2018
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The Organic Chemistry Tutor
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Product Rule For Derivatives

TL;DR

The video explains the product rule for finding derivatives, using examples with functions and trigonometric functions.

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Questions & Answers

Q: What is the product rule for finding derivatives?

The product rule states that if we have a function f multiplied by another function g, the derivative of f times g is f'g + fg'.

Q: How do you use the product rule to find derivatives?

To use the product rule, first find the derivatives of each individual function. Then, plug them into the product rule formula: f'g + fg'. Simplify the expression if possible.

Q: Can you give an example of using the product rule for finding a derivative?

Sure, let's take the example of finding the derivative of x^2 * sin(x). The derivative of x^2 is 2x, and the derivative of sin(x) is cos(x). Using the product rule formula, we get the derivative as 2xsin(x) + x^2cos(x).

Q: How do you simplify the expression after applying the product rule?

After applying the product rule, you can simplify the expression by factoring out common factors or combining like terms. If further simplification is not possible, you can leave the expression as it is.

Summary & Key Takeaways

  • The product rule states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

  • The video provides examples of using the product rule for finding derivatives, including examples with polynomial expressions and trigonometric functions.

  • The process involves finding the derivatives of each individual function, plugging them into the product rule formula, and simplifying the resulting expression.

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