Find dydt using the chain rule y x2 x 2t5SolutionUsing t

Find dy/dt using the chain rule : y = x^2 , x = 2t-5

Solution

Using the chain rule we know that for a function y = f(x) where x = f(t), dy / dt = dy / dx * dx / dt.

Now we have the functions: y = x^2 , x = 2t-5

For y =x^2, dy/dx = 2x

For x = 2t-5, dx /dt = 2

So dy/dt = dy/dx * dx/dt

=> 2x * 2 = 4x

=> 4* ( 2t-5)

=> 8t