Differentiate y=2t+3 and x=t^2 -t

In summary, to differentiate the given functions and express the answer in factored form, you would first find dy/dx = (dy/dt)/(dx/dt) and then use the rules of differentiation to calculate dy/dt and dx/dt. Once you have those values, you can use the factored form of the functions to express your final answer.
  • #1
jay17jay
7
0

Homework Statement


Differentiate each function and if possible express your answer in factoring form
y=2t+3 and x=t^2 -t

Homework Equations





The Attempt at a Solution


im really lost on this question but this is what i did so far
x=t(t-1)
x/t-1=t
so: y=2(x/t-1)+3
but now I am lost because that seems wrong you can't have two variables right??
 
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  • #2
Instead of factoring it first, just differentiate them both with respect to t.

y=2t+3 and x=t^2 -t


Remember your rules of differentiation? If y=xn then dy/dx =nxn-1.
 
  • #3
oh ok so:
dy/dx=2
dy/dx=2t-1
but then what...
 
  • #4
jay17jay said:
oh ok so:
dy/dx=2
dy/dx=2t-1
but then what...

I think you mean dy/dt=2, and dx/dt=2t-1. And what does it mean to "express your answer in factoring form"?
 
  • #5
sorry yes in respect to t.
the questions just states when possible express you answer in factored form.
 
  • #6
jay17jay said:
sorry yes in respect to t.
the questions just states when possible express you answer in factored form.

Then I believe you're done. Unless you're also expected to find dy/dx.
 
  • #7
yes i think am suppose to do that and that's where I am confused how do i combine them?
the question says "if y=2t+3 and x+t^2 -t, find dy/dx"
 
  • #8
dy/dx = (dy/dt)/(dx/dt), if I recall correctly.
 
  • #9
perfect thankyou :)
 
  • #10
Char. Limit said:
dy/dx = (dy/dt)/(dx/dt), if I recall correctly.

Your recollection is correct. If y is a function of x, and x is a function of t, then dy/dt = dy/dx * dx/dt.

Solve this equation for dy/dx to get dy/dx = (dy/dt)/(dx/dt).
 

Related to Differentiate y=2t+3 and x=t^2 -t

1. What is the first step in differentiating the given equation?

The first step in differentiating y=2t+3 and x=t^2 -t is to separate the equation into two separate functions, one for y and one for x.

2. What rule of differentiation should be applied to the equation?

The rule of differentiation that should be applied to this equation is the sum or difference rule, which states that the derivative of a sum or difference of two functions is equal to the sum or difference of their derivatives.

3. How do you differentiate y=2t+3?

To differentiate y=2t+3, you first need to identify the derivative of the constant term (3), which is 0. Then, you apply the power rule for derivatives to the variable term (2t), which is equal to 2. Therefore, the final derivative of y=2t+3 is 2.

4. How do you differentiate x=t^2 -t?

To differentiate x=t^2 -t, you first need to apply the power rule for derivatives to the variable term (t^2), which is equal to 2t. Then, you apply the power rule again to the variable term (t), which is equal to 1. Finally, you subtract 1 from the exponent of t to get the final derivative of x=t^2 -t, which is 2t-1.

5. What is the final result of differentiating y=2t+3 and x=t^2 -t?

The final result of differentiating y=2t+3 and x=t^2 -t is the set of two derivatives, dy/dt=2 and dx/dt=2t-1, representing the instantaneous rates of change for y and x respectively.

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