Differentiate y = x³Vx. EXAMPLE 8 SOLUTION Since both the base and the exponent are variable, we use logarithmic differentiation: In y = In( x³Vx) = 3V In(x) * = 3V. + (In(x)) · y 3 In(x) y' = y + Another method is to write x³Vx = eln( d dx %3D dx %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 45E
icon
Related questions
Topic Video
Question

 Differentiate y = x3√x

 

Differentiate y = x³Vx.
EXAMPLE 8
SOLUTION
Since both the base and the exponent are variable, we use logarithmic differentiation:
In y = In x³V
= 3Vx In(x)
+ (In(x)) ·
y
3 In(x)
rod
y' = y
%3D
Another method is to write x³Vx =
x3 v
dx
dx
%3D
Transcribed Image Text:Differentiate y = x³Vx. EXAMPLE 8 SOLUTION Since both the base and the exponent are variable, we use logarithmic differentiation: In y = In x³V = 3Vx In(x) + (In(x)) · y 3 In(x) rod y' = y %3D Another method is to write x³Vx = x3 v dx dx %3D
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Fundamentals of Trigonometric Identities
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
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning