How do you apply the Chain Rule to find the derivative of $$f(t) = (t^2 + 2t)^5$$ ?

To apply the Chain Rule, first identify the outer function $$f(u) = u^5$$ and the inner function $$g(t) = t^2 + 2t$$ . Then, the derivative is $$f$$ .

What is the derivative of $$y = (2x + 1)^{10}$$ ?

Using the Chain Rule, the derivative is $$y$$ .

How do you differentiate $$f(x) = (x^3 - 2x)^2$$ ?

Using the Chain Rule, the derivative is $$f$$ .

Explain the importance of the Chain Rule in calculus.

The Chain Rule is crucial for differentiating complex functions, allowing for the analysis of rates of change in composite functions.

What is the outer function in $$f(t) = (t^2 + 2t)^5$$ ?

The outer function is $$f(u) = u^5$$ , where $$u = t^2 + 2t$$ .

What is the inner function in $$f(t) = (t^2 + 2t)^5$$ ?

The inner function is $$g(t) = t^2 + 2t$$ .

Provide an example of a function that requires the Chain Rule to differentiate.

An example is $$f(x) = (3x^2 + 1)^4$$ , which requires the Chain Rule to find its derivative.

2.5 Chain Rule Only Flashcards

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1.

FLASHCARD QUESTION

Front

What is the Chain Rule in calculus?

Back

2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

Front

What is the formula for the Chain Rule?

Back

7.

FLASHCARD QUESTION

Front

When should you use the Chain Rule?

Back

Use the Chain Rule when differentiating a composite function, where one function is nested inside another.

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