# Product rule with chain rule (derivation wrt time)

• Innuendo
In summary, the product rule with chain rule is a method of finding the derivative of a function that is the product of two or more functions. To apply it, you first identify the two functions being multiplied, then take the derivative of each separately and multiply them together. This method can be applied to any number of functions and is commonly used in physics, engineering, and finance.
Innuendo
I'm trying to find the derivative of 0 = 3xcosƟ with respect to time.

I know I should use the product rule for x and cosƟ. But I don't know what I should do with the constant 3.

would it be like this?

0 = 3x(-sinƟ)(dƟ/dt) + 3(dx/dt)(cosƟ)

Yes, that's correct.

thank you

## 1. What is the product rule with chain rule in terms of differentiation?

The product rule with chain rule is a method of finding the derivative of a function that is the product of two or more functions. It states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function.

## 2. How do you apply the product rule with chain rule in practice?

To apply the product rule with chain rule, you first identify the two functions that are being multiplied together. Then, you take the derivative of each function separately using the product rule. Finally, you multiply the two derivatives together and simplify to get the final derivative.

## 3. What is the difference between the product rule and chain rule?

The product rule and chain rule are both methods of finding derivatives. The product rule is used when you have the product of two or more functions, while the chain rule is used when you have a function within a function. The chain rule is essentially an extension of the product rule.

## 4. Can the product rule with chain rule be applied to more than two functions?

Yes, the product rule with chain rule can be applied to any number of functions that are being multiplied together. The same principles apply, where you find the derivative of each function separately and then multiply them together.

## 5. How is the product rule with chain rule used in real-world applications?

The product rule with chain rule is commonly used in physics, engineering, and other fields of science to find the rate of change of a function with respect to time. It is also used in finance to calculate the sensitivity of a portfolio to changes in different variables.

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