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The function = 6x-10=2(3x-5) is the com...

The function `= 6x-10=2(3x-5)` is the composite of the functions `y=2u` and `u =3x-5` . How are the derivatives of the derivaties of these three functions related ?

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We have `(dy)/(dx) = 6 , (dy)/(du) = 2, (du)/(dx) = 3`
Since `6 = 2 xx 3" " (dy)/(dx) = (dy)/(du)cdot (du)/(dx)`
Is it an accident that `(dy)/(dx) = (dy)/(du) cdot (du)/(dx)` ?
If we think of the derivative as a rate of change, our intution allows us to see that this relationship is reasonable. For `y = f(u) and u = g(x)`, if y changes twice as fast as u and u changes three times as fast as x, then we expect y to change six times as fast as x.
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