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Mastering Derivatives in Calculus

Authored by yasin mahmud

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12th Grade

Mastering Derivatives in Calculus
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15 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Calculate the derivative of f(x) = 3x^4 - 5x^2 + 2.

3x^3 - 5x^2 + 2

12x^2 - 10

12x^3 - 10x

6x^3 - 5x

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using the product rule, find the derivative of f(x) = (2x^3)(x^2 + 1).

10x^4 + 6x^2

4x^3 + 2x^2

6x^5 + 2x

8x^4 + 4x^2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Apply the quotient rule to find the derivative of f(x) = (x^2 + 1)/(x - 3).

(x^2 - 6x - 1)/(x - 3)^2

(x^2 + 6x + 1)/(x - 3)^2

(2x)/(x - 3)

(x^2 - 1)/(x + 3)^2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Use the chain rule to differentiate f(x) = sin(3x^2 + 2).

f'(x) = 6x * cos(3x^2 + 2)

f'(x) = 6 * cos(3x^2 + 2)

f'(x) = 3x * cos(3x^2 + 2)

f'(x) = 9x^2 * sin(3x^2 + 2)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the second derivative of f(x) = x^5 - 4x + 7.

12x^2 - 4

15x^4

5x^6

20x^3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Calculate the derivative of f(x) = e^(2x) * ln(x).

f'(x) = e^(2x) * (2ln(x) + 1/x)

f'(x) = e^(2x) * (ln(x) + 2)

f'(x) = e^(2x) * (2/x)

f'(x) = 2e^(2x) * ln(x)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Using the product rule, find the derivative of f(x) = (x^2 + 3)(x^3 - 2).

4x^4 + 6x^2 - 2x

5x^4 + 6x^2 - 4x

5x^4 + 9x^2 - 4x

3x^4 + 9x^2 - 6

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