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Differentiation with COS

Let y=4cos(x) and x be a function of t such that dx/dt = 3e^(2t) and x = 3/2 when t = 0.
The value of dy/dt when x = pi/2 is: ??
can someone please help - i have no clue how to solve this.
(edited 10 years ago)
Original post by confusedinmaths
Let y=4cos(x) and x be a function of t such that dx/dt = 3e^(2t) and x = 3/2 when t = 0.
The value of dy/dt when x = ?/2 is: ??
can someone please help - i have no clue how to solve this.


dydt=dydx×dxdt\displaystyle \frac{dy}{dt}=\frac{dy}{dx} \times \frac{dx}{dt}
Original post by Mr M
dydt=dydx×dxdt\displaystyle \frac{dy}{dt}=\frac{dy}{dx} \times \frac{dx}{dt}



thats the easy bit, its the putting all the facts together that isnt working out ;P
but i dont get how the two equations relate! :frown:

from y = to the dx/dt --- what is this referring to?
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Avatar for Liamnut
Liamnut
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You have dx/dt=3e^2t. You can work out dy/dx using y=4cosx.

Multiply then together to get dy/dt, it will be an expression in terms if t and x.

Then you can plug your x value and t value in.
Original post by confusedinmaths
Let y=4cos(x) and x be a function of t such that dx/dt = 3e^(2t) and x = 3/2 when t = 0.
The value of dy/dt when x = ?/2 is: ??
can someone please help - i have no clue how to solve this.


Show your working. You may need to find x in terms of t by integration but it is hard for us to be sure as the question is not completely readable (you have x = ?/2 and x = 3/2 and I'm not sure if these are supposed to be the same or involve pi and I can't be bothered to guess).
fixed it. and i dont even know where to begin? integrate dx/dt? but will that tell me x in 4cos(x)??? what does it tell me ?
Original post by liamnut
you have dx/dt=3e^2t. You can work out dy/dx using y=4cosx.

Multiply then together to get dy/dt, it will be an expression in terms if t and x.

Then you can plug your x value and t value in.



oh thats helps! Thanks
Original post by confusedinmaths
fixed it.


Find dydt\frac{dy}{dt} using the rule I gave you in my first post.

Find x in terms of t by integrating dxdt\frac{dx}{dt} with respect to t. Substitute in the values provided to solve your constant of integration.

Find the value of t when x = pi/2.

Now substitute these values into the equation you obtained at the start.

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