What is the product rule for differentiation?

The product rule states that if $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}[u(x)v(x)] = u$$ .

What is the quotient rule for differentiation?

The quotient rule states that if $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{d}{dx}\left[\frac{u(x)}{v(x)}\right] = \frac{u$$ .

What is the chain rule for differentiation?

The chain rule states that if $$y = f(g(x))$$ , then $$\frac{dy}{dx} = f$$ .

What is the derivative of sin(x)?

The derivative of $$\sin x$$ is $$\cos x$$ .

What is the derivative of cos(x)?

The derivative of $$\cos x$$ is $$-\sin x$$ .

What is the derivative of e^x?

The derivative of $$e^x$$ is $$e^x$$ .

What is the derivative of tan(x)?

The derivative of $$\tan x$$ is $$\sec^2 x$$ .

What is the relationship between a function and its derivative?

The derivative of a function provides information about the function's slope and concavity at any given point.

Derivatives Memory Flashcard 2 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the limit definition of a derivative?

Back

2.

FLASHCARD QUESTION

Front

What must you add when doing implicit differentiation for terms containing y?

Back

3.

FLASHCARD QUESTION

Front

What is the derivative of ln(x)?

Back

4.

FLASHCARD QUESTION

Front

What is the derivative of log_a(x) given that a > 0 and a ≠ 1?

Back

5.

FLASHCARD QUESTION

Front

What is the derivative of arccos(x)?

Back

6.

FLASHCARD QUESTION

Front

What does the derivative represent in calculus?

Back

The derivative represents the rate of change of a function with respect to a variable.

7.

FLASHCARD QUESTION

Front

What is the power rule for differentiation?

Back

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