In this case, we let *u* = *x*^{2} + 3 and
then *y* = *u*^{5}.

We see that:

*u*is a function of*x*and*y*is a function of*u.*

For the **chain rule**, we firstly need to find `(dy)/(du)` and `(du)/(dx)`:

`(dy)/(du)=5u^4=5(x^2+3)^4`; and

`(du)/(dx)=2x`

So

`(dy)/(dx)=(dy)/(du)(du)/(dx)`

`=5(x^2+3)^4(2x)`

`=10x(x^2+3)^4`

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