Derivative Power Rule and Def of Derivative Flashcards

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1.

FLASHCARD QUESTION

Front

What is the Derivative Power Rule?

Back

The Derivative Power Rule states that if $f(x) = x^n$ , then the derivative $f'(x) = nx^{n-1}$ .

2.

FLASHCARD QUESTION

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

3.

FLASHCARD QUESTION

Front

Differentiate $y = x^3$ .

Back

$y' = 3x^2$ .

4.

FLASHCARD QUESTION

Front

Differentiate $y = 5x^4 - 3x^2 + 2$ .

Back

$y' = 20x^3 - 6x$ .

5.

FLASHCARD QUESTION

Front

What is the derivative of a constant?

Back

The derivative of a constant is zero.

6.

FLASHCARD QUESTION

Front

Differentiate $y = 1/x$ .

Back

$y' = -x^{-2}$ .

7.

FLASHCARD QUESTION

Front

Differentiate $y = 2x^{-3}$ .

Back

$y' = -6x^{-4}$ .

8.

FLASHCARD QUESTION

Front

What is the slope of the tangent line to $y = x^2$ at $x = 3$ ?

Back

@@y' = 2x ightarrow y' = 2(3) = 6@@.

9.

FLASHCARD QUESTION

Front

Differentiate $y = \frac{1}{\text{sqrt}(x)}$ .

Back

$y' = -\frac{1}{2}x^{-3/2}$ .

10.

FLASHCARD QUESTION

Front

What is the derivative of $y = \text{sin}(x)$ ?

Back

$y' = \text{cos}(x)$ .

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