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mathland

Member

Registered: 2021-03-25

Posts: 444

Derivative of Composite Functions

Write y as a function of x. Find dy/dx using
the Chain Rule.

1. y = u^3, u = 3v^2 + 1, v = 4/x2

2. y = u^2 + 1, u = 4/v
v = x^2

For both problems, I need to find

dy/dx = (dy/du)(du/dv)(dv/dx)

Can someone get me started on each question?

Thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Derivative of Composite Functions

Start by doing the three differentiations.

'Chain' then together to create an expression for dy/dx.

Maybe you could stop at that, but I expect you should also put the final answer in terms of x only (if possible).

So eliminate 'u' by writing any u bits in terms of v.  Simplify if poss.

Then eliminate v by writing any v bits in terms of x.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Derivative of Composite Functions

Start by doing the three differentiations.

'Chain' then together to create an expression for dy/dx.

Maybe you could stop at that, but I expect you should also put the final answer in terms of x only (if possible).

So eliminate 'u' by writing any u bits in terms of v.  Simplify if poss.

Then eliminate v by writing any v bits in terms of x.

Bob

You said:

"So eliminate 'u' by writing any u bits in terms of v.  Simplify if poss.

Then eliminate v by writing any v bits in terms of x."

What do you mean here?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Derivative of Composite Functions

Please post your answer as far as you have got.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Derivative of Composite Functions

Please post your answer as far as you have got.

Bob

I will show my work here from now on, wrong or right.