Understanding the Chain Rule for Derivatives

Thread starter oswald
Start date Mar 18, 2009
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Chain Chain rule

In summary, the chain rule is a mathematical rule used to find the derivative of a composite function. To apply the chain rule, you first identify the outer function and the inner function, take the derivative of the outer function, multiply it by the derivative of the inner function, and replace the inner function with its original expression. The chain rule is important because it allows us to find the derivative of complex functions. It can be used with any type of function, but not with non-differentiable functions. The chain rule and the product rule are two different rules used for finding derivatives.

Mar 18, 2009

oswald

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The Attempt at a Solution

My dought is about if

,dw/dy*dy/dt = (-2)t^(-3)*dy/dt

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Mar 18, 2009

Dick

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Why is your working under copyright? And why does the solution look nothing like that? And why is there no problem stated?

1. What is the chain rule derivative?

The chain rule is a mathematical rule used to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

2. How do you apply the chain rule?

To apply the chain rule, you first identify the outer function and the inner function of the composite function. Then, you take the derivative of the outer function and multiply it by the derivative of the inner function. Finally, you replace the inner function with its original expression to get the final derivative.

3. Why is the chain rule important?

The chain rule is important because it allows us to find the derivative of complex functions by breaking them down into simpler functions. This is especially useful in physics and engineering where many real-world problems can be modeled using composite functions.

4. Can the chain rule be used with any type of function?

Yes, the chain rule can be used with any type of function, including trigonometric, exponential, and logarithmic functions. However, it is important to note that the chain rule is not applicable to all types of functions, such as non-differentiable functions.

5. Is the chain rule the same as the product rule?

No, the chain rule and the product rule are two different rules used to find the derivatives of functions. The product rule is used when finding the derivative of a product of two functions, while the chain rule is used when finding the derivative of a composite function.