Chain Rule and Composite Functions Quiz

Question 1 / 11

🏆 Rank #-- ▾

0 %

0/100

Score 0/100

1) What is the derivative of y = (2x + 3)⁴?

4(2x + 3)³

6(2x + 3)³

8(2x + 3)³

8(2x + 3)⁴

Differentiate the outer function, then multiply by the derivative of 2x + 3. y′ = 4(2x + 3)³ × 2 = 8(2x + 3)³

Explanation

Differentiate the outer function, then multiply by the derivative of 2x + 3. y′ = 4(2x + 3)³ × 2 = 8(2x + 3)³

About This Quiz

Chain Rule and Composite Functions Quiz - Quiz

Differentiation is the derivative of a function of a real variable measuring the sensitivity to change of the function value. In this quiz, you will see how well do you understand the basic rules of differentiation and composite function. This quiz is specially designed to improve a person's mathematical skills.... see moreGo for it! see less

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) In y = (x² + 5)³, what is the inner function?

X² + 5

(x² + 5)²

X²

The expression inside the outer power is x² + 5, so it is the inner function.

Explanation

The expression inside the outer power is x² + 5, so it is the inner function.

3) Complete the derivative: y = (3x − 1)⁵, y′ = 5(3x − 1)⁴ × _____

The derivative of the inner function 3x − 1 is 3.

Explanation

The derivative of the inner function 3x − 1 is 3.

4) Which function requires the chain rule?

Y = x⁴

Y = 5x + 2

Y = (x + 1)⁴

Y = 7

This function contains one function inside another. The power is applied to the inner expression x + 1.

Explanation

This function contains one function inside another. The power is applied to the inner expression x + 1.

5) A student differentiates y = (x² + 1)³ as y′ = 3(x² + 1)². What is missing?

The exponent should stay 3

The derivative of x² + 1

The constant 1

A negative sign

The student must also multiply by the derivative of the inner function, which is 2x. The correct derivative is: y′ = 6x(x² + 1)²

Explanation

The student must also multiply by the derivative of the inner function, which is 2x. The correct derivative is: y′ = 6x(x² + 1)²

6) Match the function with its derivative. Function: y = (5 − x)³

3(5 − x)²

−3(5 − x)²

−5(5 − x)²

3(5 − x)³

The derivative of 5 − x is −1. y′ = 3(5 − x)² × (−1) = −3(5 − x)²

Explanation

The derivative of 5 − x is −1. y′ = 3(5 − x)² × (−1) = −3(5 − x)²

7) If y = (x + 2)³, what is the value of y′ when x = 0?

First find the derivative: y′ = 3(x + 2)². Now substitute x = 0: y′ = 3(2)² = 12

Explanation

First find the derivative: y′ = 3(x + 2)². Now substitute x = 0: y′ = 3(2)² = 12

8) Which is the correct first step for differentiating y = √(4x + 1)?

Rewrite it as y = (4x + 1)²

Rewrite it as y = (4x + 1)¹ᐟ²

Rewrite it as y = 1 ÷ (4x + 1)

Rewrite it as y = 4x¹ᐟ² + 1

Writing the square root as a fractional power makes it easier to apply the power rule and chain rule.

Explanation

Writing the square root as a fractional power makes it easier to apply the power rule and chain rule.

9) The derivative of y = (x³ + 2)² is 6x²(x³ + 2).

True

False

y′ = 2(x³ + 2) × 3x² = 6x²(x³ + 2)

Explanation

y′ = 2(x³ + 2) × 3x² = 6x²(x³ + 2)

10) Which derivative is incorrect?

Y = (x + 1)², y′ = 2(x + 1)

Y = (2x + 1)³, y′ = 6(2x + 1)²

Y = (x² + 3)², y′ = 4x(x² + 3)

Y = (4x − 1)², y′ = 2(4x − 1)

The derivative of the inner function 4x − 1 is 4, so the correct derivative is: y′ = 2(4x − 1) × 4 = 8(4x − 1)

Explanation

The derivative of the inner function 4x − 1 is 4, so the correct derivative is: y′ = 2(4x − 1) × 4 = 8(4x − 1)

Thank you for your feedback!