If z^2=x^2+y^2 with z0, dx/dt=3, and dy/dt=6, find dz/dt when x=4 and y=3.

Question

If z^2=x^2+y^2 with z>0, dx/dt=3, and dy/dt=6, find dz/dt when x=4 and y=3.

anonymous · Answer

@ranga @zepdrix

anonymous · Answer

@phi

phi · Answer

take the derivative with respect to t  (implicit differentiation)

do you know how to do that ?

anonymous · Answer

yes but thats what i thought i should do but then whats the point of all the other info

phi · Answer

First, what do you get for the d/dt  of that equation ?

anonymous · Answer

there is no t in the equation so how do i do d/dt

phi · Answer

use the "rule"  d/dt  of a variable   (x , y or z)  is dx/dt,  dy/dt or dz/dt
 use the chain rule where needed:  example  d/dt  x^2  = 2 x  dx/dt

anonymous · Answer

ok. so its 2zz'=2xx'+2yy'

phi · Answer

yes.  notice that with the original equation
z^2 = x^2 + y^2
you can find z (given x and y)
they tell you x'  and y'
so fill in the numbers in your derivative and solve for z'

anonymous · Answer

how do i find z and y

phi · Answer

x=4 and y=3.

phi · Answer

z^2=x^2+y^2

phi · Answer

*** that should answer your question
" whats the point of all the other info?"
****

anonymous · Answer

z'=30/sqrt21?

phi · Answer

x=4, y= 3, z=5, x'=3,  y'=6
5 z'=4*3+3*6=12+18= 30
z'= 6

anonymous · Answer

ok thanks

phi · Answer

you should remember that 3^2 + 4^2= 5^2   (3,4,5 right triangle triplet)
not sure how you get 21 out of that

anonymous · Answer

yeah i really messed up somewhere. thanks though