Mastering Differentiation Concepts

Mastering Differentiation Concepts

12th Grade

15 Qs

quiz-placeholder

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Mastering Differentiation Concepts

Mastering Differentiation Concepts

Assessment

Quiz

Others

12th Grade

Practice Problem

Hard

Created by

Noman Mobin

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of f(x) = 3x^2 + 5?

6x

3x

5x

6x^2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

8x^3 + 2

2x^4 + 2

8x^2 + 3

6x^3 + 2

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Differentiate the function f(x) = x^4 - 4x^3 + 6x - 1.

4x^3 - 10x^2 + 7

4x^3 - 12x^2 + 6

3x^3 - 12x^2 + 5

4x^3 - 8x^2 + 6

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

(2x)/(x - 1)

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

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the chain rule and how is it applied in differentiation?

The chain rule is a method for finding the area under a curve by averaging the values of the function.

The chain rule allows us to differentiate composite functions by multiplying the derivatives of the outer and inner functions.

The chain rule is used to integrate functions by adding the derivatives of the outer and inner functions.

The chain rule states that the derivative of a function is always zero regardless of its composition.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Find the second derivative of f(x) = sin(x).

sin(2x)

cos(x)

-cos(x)

-sin(x)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Differentiate the function f(x) = e^(2x) using the chain rule.

2e^(2x)

e^(x)

4e^(2x)

e^(2x)

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