Second Derivative parametric function

Calculus Tutorial

Second Derivative parametric function

Intro

x=u(t)
dx/dt=U'(t)
y=v(t)
dy/dt=v'(t)
dy/dx=dy/dt.dt/dx
d2y/dx2=d/dt(dy/dx).dt/dx

Sample Problem

x=2e(3t),y=e(2t)+1
find d2y/dx2

Solution

dx/dt=2.e(3t).3
=6e(3t)
y=e(2t)+1
dy/dt=e(2t).2
=2e(2t)
dy/dx=dy/dt.dt/dx
=2e(2t)/6e(3t)
=e(2t-3t)/3
=e(-t)/3
d2y/dx2=d/dt(dy/dx).dt/dx
=d/dt(e(-t)/3).dt/dx
=-e(-t)/3.(1/6e(3t))
=-1/18.(e(-t-3t))
=-1/18.(e(-4t))
=-1/18e(4t)
=-e(-4t)/18



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 teacher\'s training college diploma in Srilanka. I completed my B.Sc degree course at Bharayiar university in India.
13 Subjects
KnowRo Tutor
28 Tutorials
Montréal, QC
Get Tutoring Info

Suggested Tutors for Calculus Help

Abdul B

Arlington, VA

Math And Science Expert

Siddarth C

Vienna, VA

All Subjects

Emily V

Alexandria, VA

Versatile And Flexible Tutor

Maxine J

Bethesda, MD

Any Topic, Any Language

^