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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

y= x^2

x= 2t-5

Now substitue with x value:

y= x^2 = (2t-5)^2

==> y= 4t^2 -20t + 25

Now let us diffrentiate:

==> dy = (8t - 20) dt

=> dy/dt  = 8t - 20

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william1941 | College Teacher | (Level 3) Valedictorian

Posted on

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 – 20

dy / dt = 8t-20

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