Differentiate: f(x) = x 7 (5 + 8x) 3

f '(x) = x 6 (5 + 8x) 2 (35 + 80x)

f '(x) = x 2 (5 + 8x) 6 (35 + 80x)

f '(x) = 8x 7 (5 + 8x) 2 (35 + 80x)

f '(x) = x 6 (5 + 8x) 3 (35 + 80x)

Unit 4 AP Calculus

Authored by S W

Mathematics

12th Grade

CCSS covered

Used 85+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

About

This quiz covers differentiation techniques in Advanced Placement Calculus, specifically focusing on the chain rule, product rule, implicit differentiation, and derivatives of exponential and logarithmic functions. The content is designed for grade 12 students who have mastered basic derivative rules and are ready to tackle composite functions and more complex differentiation scenarios. Students need a solid understanding of the power rule, trigonometric derivatives, and exponential functions as prerequisites. The problems require students to recognize when to apply the chain rule for composite functions like (x⁶ + 4)⁵, use the product rule for expressions such as x⁷(5 + 8x)³, and navigate implicit differentiation when variables cannot be easily separated. The inclusion of logarithmic differentiation and exponential functions with variable exponents demonstrates the comprehensive nature of differential calculus at the AP level. Created by S W, a Mathematics teacher in US who teaches grade 12. This assessment serves as an excellent unit review or practice tool for students preparing for the AP Calculus exam, particularly for Unit 4 content covering advanced differentiation techniques. Teachers can deploy this quiz as a formative assessment to identify students who need additional support with chain rule applications or implicit differentiation before moving to integration topics. The variety of problem types makes it ideal for homework assignments, allowing students to practice different differentiation scenarios independently, or as a warm-up activity to reinforce previously learned concepts. This quiz aligns with Common Core standards HSF-IF.C.7 and HSA-CED.A.2, as well as College Board AP Calculus AB standards covering derivatives of composite, implicit, and transcendental functions.

Content View

Student View

25 questions

Show all answers

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the derivative of f(x) = (x⁶ + 4)⁵

f '(x) = 5x⁵(x⁴ + 4)⁴

f '(x) = 6x⁵(x⁶ + 4)⁴

f '(x) = 30x⁵(x⁶ + 4)⁴

f '(x) = 30x⁶(x⁶ + 4)⁴

MULTIPLE CHOICE QUESTION

5 mins • 12 pts

Find the derivative of f(x)=(x³-2x)²

6x⁵ - 12x³+8x

6x⁵ - 16x³+8x

x⁶-4x⁴+4x²

6x⁵ - 16x^3-8x

find y' for y=(e^5x)+1

5e^5x+1

e^5x

5e^5x

find y' for y= sin(2x²)

4sin(2x²)

4xcos(2x²)

2xcos(2x²)

xcos(4x²)

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

Differentiate:
f(x) = x⁷ (5 + 8x)³

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

6 -x

3x² +3y²

−x²/y²

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

20 questions

Discrete Distribution

Quiz

•

12th Grade - University

20 questions

五年级数学复习

Quiz

•

1st Grade - University

20 questions

ASESMEN SUMATIF TENGAH SEMESTER

Quiz

•

9th Grade - University

20 questions

SNBT [PEM : Penalaran Matematika]

Quiz

•

12th Grade

20 questions

Part 2: Unit 2 Review

Quiz

•

10th Grade - University

20 questions

AP Statistics Vocabulary Quiz Chapters 1,2,3

Quiz

•

12th Grade

20 questions

Dominio Matemático 1

Quiz

•

12th Grade

21 questions

SIMULACRO DE MATEMÁTICAS PRUEBA SABER 11

Quiz

•

11th Grade - Professi...

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

54 questions

Analyzing Line Graphs & Tables

Quiz

•

4th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

Discover more resources for Mathematics

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

15 questions

Exponential Growth and Decay Word Problems Practice

Quiz

•

9th - 12th Grade

17 questions

Explore Experimental and Theoretical Probability

Quiz

•

7th - 12th Grade

15 questions

Parallelogram Properties

Quiz

•

10th - 12th Grade

18 questions

Solving Systems- Word Problems

Quiz

•

9th - 12th Grade

34 questions

7.4 Review Cubic and Cube Root Functions

Quiz

•

10th - 12th Grade

21 questions

Geometry Chapter 2 Review

Quiz

•

9th - 12th Grade

9 questions

Identifying Parts Of An Expression

Quiz

•

6th - 12th Grade