Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
Related questions
Topic Video
Question
100%
![Find the derivative of the function. Simplify and express the answer using positive exponents only.
R(x) = [x²(x² + 7x)]ª
Step 1
We want to find the derivative of the function R(x) = [x²(x² + 7x)]ª, simplifying and expressing the answer
using positive exponents only.
We begin by raising both factors inside the brackets to the fourth power. This gives
8
R(x) = x
(x2 + 7x)
Step 2
We now proceed to take the derivative. Since we rewrote our function as a product of two functions, the first
rule we use will be the Product
Rule. While using this rule, we will have to also use the Chain
Rule.
ra) = x* acx² + 7x)*( 4x + 21
D +
(x² + 7x)*(8x7)
= 4(x2 + 7x)3
4
+ (x2 + 7x)2x7
(x² + 7x)³[x(2x + 7) + 2(x2 + 7x)]
4x
( d/dx
(x² + 7x)³|
x2 + 7
= 4x
11
x+7
3
4х + 21](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f2c69a7-cd99-4b72-b7d6-59c73cbf078b%2F6396607d-fff9-4ac2-ac4e-05167b230994%2Fa3uh3ue_processed.png&w=3840&q=75)
Transcribed Image Text:Find the derivative of the function. Simplify and express the answer using positive exponents only.
R(x) = [x²(x² + 7x)]ª
Step 1
We want to find the derivative of the function R(x) = [x²(x² + 7x)]ª, simplifying and expressing the answer
using positive exponents only.
We begin by raising both factors inside the brackets to the fourth power. This gives
8
R(x) = x
(x2 + 7x)
Step 2
We now proceed to take the derivative. Since we rewrote our function as a product of two functions, the first
rule we use will be the Product
Rule. While using this rule, we will have to also use the Chain
Rule.
ra) = x* acx² + 7x)*( 4x + 21
D +
(x² + 7x)*(8x7)
= 4(x2 + 7x)3
4
+ (x2 + 7x)2x7
(x² + 7x)³[x(2x + 7) + 2(x2 + 7x)]
4x
( d/dx
(x² + 7x)³|
x2 + 7
= 4x
11
x+7
3
4х + 21
Expert Solution
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage