Parametric Curves – Finding Second Derivatives. The formula and one relatively simply example are shown! For more free math videos, visit http://JustMathTutoring.com.

30 Responses to “Parametric Curves – Finding Second Derivatives”

My book doesn’t explain the intuition behind this at all, so I don’t get
why this formula ends up the way it is. how does d/dx(dy/dt / dx/dt) end up
with dx/dt in the denominator? how does d/dx(dx/dt) = dx/dt?

Because that would give you the second derivative in respect to t, not to
x. It would give you (d/dt)(dy/dx), not (d/dx) (dy/dx). In order to do
(d/dx)(dy/dx), you can say (d/dt)(dy/dx)(dt/dx) , from that, the dt’s would
cancel out to give you (d/dx) (dy/dx).

Patrick, where may i learn all of these simplification rules you use when
there is a fraction divided by another number? Such as what you did at 3:30
with making the denominator (3t^2+1)^3?

Omg I finally understand it, thank you so much!

BOSS

My book doesn’t explain the intuition behind this at all, so I don’t get

why this formula ends up the way it is. how does d/dx(dy/dt / dx/dt) end up

with dx/dt in the denominator? how does d/dx(dx/dt) = dx/dt?

Thank you so much

Here is an example of finding a second derivative for parametric equations.

Thank you so much =D

Chapter 10 section 1 is now my bitch. Thank you.

THANK YOU BOSS

This video was more helpful than my teacher talking for two hours about

this. Really appreciate your help! Thanks!

sweet! now if only it worked the same way for the students in my class…

maybe i should turn on my videos instead of teaching! good luck on the

exam!!

GREAT ! THATS HOW OUR TEACHER TEACH BUT DEFINITELY YOUR MORE UNDERSTANDABLE

! )))

it is said that a positive 2nd derivative => concave up and negative =>

concave down. Convex is not used in that sense

thank you so much

thank youuuuuuuuu ^^

goooooooood luck!

Your rock , this helped me a lot!!

omg its easy like 1 2 3!!! yayyyyyyyy

I am so not going to fail my calculus test tomorrow. Wow, thank you so

much, it just all clicked into place in my head.

Because that would give you the second derivative in respect to t, not to

x. It would give you (d/dt)(dy/dx), not (d/dx) (dy/dx). In order to do

(d/dx)(dy/dx), you can say (d/dt)(dy/dx)(dt/dx) , from that, the dt’s would

cancel out to give you (d/dx) (dy/dx).

How come in finding the second derivative, we don’t just take the

derivative again of the result we got for the first derivative?

so you say you’re trying to become a mechanical engineer…

What is the answer if dx/dt is 0? can it not be done?

@mihooo123 he’s correct, i don’t think you did your math right.

THANK YOU!!!!!!!!!

Patrick, where may i learn all of these simplification rules you use when

there is a fraction divided by another number? Such as what you did at 3:30

with making the denominator (3t^2+1)^3?

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