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

[jay17jay]

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??

 

[rock.freak667]

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 =nx^n-1.

 

[jay17jay]

oh ok so:
dy/dx=2
dy/dx=2t-1
but then what...

 

[Char. Limit]

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"?

 

[jay17jay]

sorry yes in respect to t.
the questions just states when possible express you answer in factored form.

 

[Mentallic]

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.

 

[jay17jay]

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"

 

[Char. Limit]

dy/dx = (dy/dt)/(dx/dt), if I recall correctly.

 

[jay17jay]

perfect thankyou :)

 

[Mark44]

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).