Understand Related Rates: Calculus Review

[daveed]

i don't really understand when you differentiate both sides of an equation to, for example, time.

like, if you have tan(x)=y/50,
you would get sec^2(x)dx/dt=1/50*(dy/dt)
so does that mean when you differentiate both sides you find the derivative of the whole term and then multiply it by dwhatever/dt?

the book I am looking at is just a review for calculus, its only got a short sentence here about this, and its confusing

 

[arildno]

Well, both x and y are functions of time.
Hence, you use the chain rule when differentiating the equation

 

[shmoe]

Yes, use the chain rule like arildno mentioned. For the problem you gave, you are thinking of x and y as functions of t. You can make this more explicit by replacing "x" with "x(t)" and "y" with "y(t)". The differentiate w.r.t time as normal. When this dependence on t is understood, texts will sometimes supress the (t) part of the notation to make things neater, like the example you gave.

 

[daveed]

oh my... lol thankyou I am new with calc-learnin it myself this summer-and managed to remember the chain rule wrong. haha thanks guys