What is the derivative of $$p = \frac{1}{\text{sqrt}(q+9)}$$ with respect to $$q$$ ?

$$\frac{dp}{dq} = -\frac{1}{2(q+9)^{\frac{3}{2}}}$$

Differentiate the function $$y = \text{sin}(2x)$$ using the chain rule.

$$\frac{dy}{dx} = 2\text{cos}(2x)$$

What is the product rule in differentiation?

The product rule states that if you have two functions multiplied together, $$f(x)g(x)$$ , then the derivative is $$f$$ .

Differentiate $$y = x^2 \text{ln}(x)$$ using the product rule.

$$\frac{dy}{dx} = 2x \text{ln}(x) + x$$

What is the quotient rule in differentiation?

The quotient rule states that if you have a function that is the quotient of two functions, $$\frac{f(x)}{g(x)}$$ , then the derivative is $$\frac{f$$ .

Differentiate $$y = \frac{x^2 + 1}{x}$$ using the quotient rule.

$$\frac{dy}{dx} = \frac{(2x)(x) - (x^2 + 1)(1)}{x^2} = \frac{x^2 - 1}{x^2}$$

What is implicit differentiation?

Implicit differentiation is a technique used to differentiate equations that define $$y$$ implicitly in terms of $$x$$ .

Differentiate the equation $$x^2 + y^2 = 1$$ implicitly with respect to $$x$$ .

@@2x + 2yrac{dy}{dx} = 0 ightarrow rac{dy}{dx} = -rac{x}{y}@@

What is the meaning of the second derivative?

The second derivative measures the rate of change of the rate of change of a function, indicating concavity.

AP Calc unit 3/4 review Flashcards

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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When do you use the chain rule in differentiation?

Back

You use the chain rule when there is a function within a function.

3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

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What is the chain rule in calculus?

Back

The chain rule is a formula for computing the derivative of the composition of two or more functions.

7.

FLASHCARD QUESTION

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