# How do you differentiate the following parametric equation: # x(t)=(lnt)^2, y(t)= -2t^2-2t^3e^(t) #?

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

To differentiate the parametric equations ( x(t) = (\ln t)^2 ) and ( y(t) = -2t^2 - 2t^3e^t ) with respect to ( t ), use the chain rule and product rule where applicable:

[ \frac{dx}{dt} = 2(\ln t)(1/t) ] [ \frac{dy}{dt} = -4t - 6t^2e^t - 2t^3e^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.

- For #f(t)= (t^3-t+1,t^2-t)# what is the distance between #f(2)# and #f(5)#?
- What is the arclength of #f(t) = (-2(t+3)^3,(t-2)^2)# on #t in [1,2]#?
- How do you differentiate the following parametric equation: # x(t)=-t-e^t, y(t)= -2t^2-2t^3e^(t) #?
- What is the derivative of #f(t) = (t +te^t, e^t-t^2+t ) #?
- How do you write the cartesian equation for x = t - 2 and y = -(t²) + t + 1?

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