Answer to Question #301866 in Calculus for kazi

Question

Given: x = 2t + 1 and y = 4t - 1. Find y’.

Answer 1

Given:

x = 2t + 1

y = 4t - 1

First, we solve the first equation for t.

2t = x-1

t= (x-1)/2

We replace t in the second equation with the expression (x-1)/2.

y = (4(x-1)/2) -1

= ((4x-4)/2) - 1

= 2x-2-1

= 2x-3

Now, we remain with one equation with variable y as the subject:

y = 2x-3

$\frac{d}{dx}$[2x-3] = y' = 2

Answer: y' = 2