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How do you differentiate the following parametric equation: # x(t)=t, y(t)=t #?

Answer 1

Luke Alvarez

seems little point as #x = t = y# meaning #y = x# so #y' = 1#

but

#dy/dx = (dy/dt)/(dx/dt) = 1/1#

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Answer 2

Paisley Johnson

To differentiate the given parametric equations x(t) = t and y(t) = t with respect to time parameter t, you differentiate each equation separately:

Differentiate x(t) with respect to t: dx/dt = d(t)/dt = 1
Differentiate y(t) with respect to t: dy/dt = d(t)/dt = 1

Therefore, the derivatives of x(t) and y(t) with respect to t are both 1.

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Answer from HIX Tutor

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.