What is the quotient rule for derivatives?

The quotient rule states that if $$u(x)$$ and $$v(x)$$ are functions, then $$\frac{u}{v}$$ .

What is the chain rule for derivatives?

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

What is the derivative of a constant function?

The derivative of a constant function is 0.

What is the derivative of sin(x)?

The derivative of sin(x) is cos(x): $$\frac{d}{dx}(\text{sin}(x)) = \text{cos}(x)$$ .

What is the derivative of cos(x)?

The derivative of cos(x) is -sin(x): $$\frac{d}{dx}(\text{cos}(x)) = -\text{sin}(x)$$ .

What is the derivative of e^x?

The derivative of e^x is e^x: $$\frac{d}{dx}(e^x) = e^x$$ .

What is the derivative of ln(x)?

The derivative of ln(x) is $$\frac{1}{x}$$ : $$\frac{d}{dx}(\text{ln}(x)) = \frac{1}{x}$$ .

What is the significance of the second derivative?

The second derivative indicates the concavity of the function and can be used to determine points of inflection.

Derivative Rules Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of a derivative?

Back

2.

FLASHCARD QUESTION

Front

What does the notation f'(x) represent?

Back

f'(x) represents the derivative of the function f at the point x.

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