anonymous
  • anonymous
please help, explanation would be greatly appreciated (picture included)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
DanJS
  • DanJS
y=2*e^cos(x) \[\frac{ dy }{ dt } = 5 unit/s\]
DanJS
  • DanJS
do a d/dt to both sides of that equation

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anonymous
  • anonymous
to which equation?
anonymous
  • anonymous
to dy/d=2(lne)(e^cosx)(-sinx)
anonymous
  • anonymous
i mean that that is the derivative of y=2e^cosx
anonymous
  • anonymous
im sorry but i dont know what that means
DanJS
  • DanJS
y is a function of x is a function of t, y--->x--->t
DanJS
  • DanJS
y ( x(t))
anonymous
  • anonymous
would t be the 5 units per second?
anonymous
  • anonymous
no nvm i know that wrong
DanJS
  • DanJS
|dw:1449434843192:dw|
DanJS
  • DanJS
to get from y to the t, you do dy/dx * dx/dt
DanJS
  • DanJS
notice that is dy/dt = (dy/dx)*(dx/dt) -- both sides same
anonymous
  • anonymous
alright what do we do next?
DanJS
  • DanJS
the thing is compounded like that \[y(x[t]) = 2e^{\cos[(x(t)]}\]
anonymous
  • anonymous
and we need to find the derivative of that equation
DanJS
  • DanJS
they give you some info dy/dx = 5 unit/s always x = pi/2 they want you to find dx/dt at the instant when the angle x(t) is pi/2
anonymous
  • anonymous
i dont understadn how i would do that
DanJS
  • DanJS
*dy/dt = 5 mistype
anonymous
  • anonymous
i still dont get it im very sorry
DanJS
  • DanJS
dy/dt = dy/dx * dx/dt take derivative w.r.t. x first, then w.r.t t
anonymous
  • anonymous
whst is w.r.t
DanJS
  • DanJS
with respect to,
DanJS
  • DanJS
dy/dt = dy/dx * dx/dt
DanJS
  • DanJS
derivative of y w.r.t.x times derivative of x w.r.t t
anonymous
  • anonymous
how am i supposed to do that if i dont know what dy/dx is or dx/dt
anonymous
  • anonymous
all i know is that dy/dt is 5 units/sec
DanJS
  • DanJS
like remember doing chain rule derivatives... you have to multiply by the derivative of the inner function ex [ d/dx] * cos(x^2+2) = -sin(x^2+2) * ( 2x)
DanJS
  • DanJS
anyway here...
anonymous
  • anonymous
thanks for trying but i have somewhere i be in an hour and i have to leave now, if i wasn't in a hurry i could probably understand it better thank you
DanJS
  • DanJS
\[\large y = 2e^{\cos(x)}\] derivative with respect to x, d/dx both sides
DanJS
  • DanJS
\[\large \frac{ dy }{ dx } = -2*\sin(x) *e^{\cos(x)}\]
DanJS
  • DanJS
a step further realizing xis a function of t, the chain rule gives you dy/dt \[\huge \frac{ d }{d t }=\frac{ dy }{ dx }*\frac{ dx }{ dt }\]
anonymous
  • anonymous
but thats what i said was the derivative at the beginning!!
anonymous
  • anonymous
so we just solve for dx/dt next?
DanJS
  • DanJS
no actual x(t) function is said, so just add that dx/dt on the end \[\frac{ dy }{ dt } = \large \frac{ dy }{ dx } * \frac{ dx }{ dt } = -2*\sin(x) *e^{\cos(x)} * \frac{ dx }{ dt }\]
DanJS
  • DanJS
use that to figure the rate x is changing with the time, dx/dt, when x is that given angle 5 = -2*sin(x)*e^(cos(x)) * [dx/dt]
DanJS
  • DanJS
\[5 = -2*\sin(\pi/2)*e^{\cos(\pi/2)}* \frac{ dx }{ dt }\]
DanJS
  • DanJS
5 = -2 * 1 * 1 * dx/dt dx/dt = 5/-2 unit/sec
DanJS
  • DanJS
just need to practice the chain rule thing for nested functions to get dy/dt you have to do d/dx first and multiply by dx/dt
DanJS
  • DanJS
like A [ B [ C [ D(x) ] ] ] same, to get to dA/dx there, you need dA/dB * dB/dC * dC/dD * dD/dx = dA*/Dx
DanJS
  • DanJS
gl

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