# How do you differentiate the following parametric equation: # x(t)=-3t/(1-t), y(t)= 1-tcost #?

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate the given parametric equations (x(t) = \frac{-3t}{1-t}) and (y(t) = 1 - t\cos(t)), we'll use the chain rule.

For (x(t)): [x'(t) = \frac{d}{dt} \left(\frac{-3t}{1-t}\right) = \frac{-3(1-t) - (-3t)(-1)}{(1-t)^2} = \frac{-3 + 3t + 3t}{(1-t)^2} = \frac{3t - 3}{(1-t)^2}]

For (y(t)): [y'(t) = \frac{d}{dt} (1 - t\cos(t)) = -\cos(t) + t\sin(t)]

So, the derivatives are: [x'(t) = \frac{3t - 3}{(1-t)^2}] [y'(t) = -\cos(t) + t\sin(t)]

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you differentiate the following parametric equation: # x(t)=1-lnt, y(t)= cost-t^2 #?
- What is the arc length of #f(t)=(3te^t,t-e^t) # over #t in [2,4]#?
- For #f(t)= (sin^2t,t/pi-2)# what is the distance between #f(pi/4)# and #f(pi)#?
- What is the arclength of #(t^2-t,t^2-1)# on #t in [-1,1]#?
- What is the arclength of #(t^2lnt,(lnt)^2)# on #t in [1,2]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7