Composite exponential function differentiation

Calculus Tutorial

Composite exponential function differentiation

Intro

product rule
chain rule
ln(a)m=m(ln)a

Sample Problem

y=(sin(x))x
find dy/dx

Solution

y=(sin(x))x
ln(y)=ln(sinx)x take(ln) both side
ln(y)=x.ln(sinx) ln(a)m=m.ln(a)
d/dx(ln(y))=d/dx(x.ln(sinx)) take derivative both side
1/y.dy/dx=1.ln(sinx)+(1/sinx).cosx.x product rule
d/dx(ln(sinx))=(1/sinx).cosx chain rule
dy/dx=y.(ln(sinx)+x.cosx/sinx) multiply by y both side
=(sin(x))x.(ln(sinx)+x.cosx/sinx) substituting y
=(sin(x))x.(ln(sinx)+x.cot(x)) simplify



About The Author

Mathematics Teacher
I was a teacher in Srilanka from 1992 to 2006.I took tuition from 1990 to 1991 in India.I do general work in Canada but I help to do homework to my daughters.I finished my teachers training college diploma in Srilanka.
Send Email
13 Subjects
KnowRo Tutor
28 Tutorials
$25
Montréal, QC
Get Tutoring Info

Suggested Tutors for Calculus Help

Ad

Varsity Tutors

(855) 475-5132 - Award-Winning Academic & Test Prep Tutors

Ad

Study Wizards

(408) 883-8660 5-Star Yelp and Google in-home tutoring

Ad

Link Educational Institute

Link Educational Institute

Lance L

Frederick, MD

Math, Chemistry And Physics Tutor

Leave a Comment

Your email address will not be published. Required fields are marked *

^