The chain rule: confusing example in book

[Becky4paws]

The following problem is an example from my textbook. I have marked * at the spot I begin to get confused.

Find the derivative dy/dx given y=1/u and u = x^2 + 5

1st step: Find dy/du which is = -u^-2.
2nd step: Find du/dx = 6x* (I thought this was where you found the derivative of u=x^2 + 5; which I computed to be 2x).

The final answer should be interms of x since the problem asked for dy/dx. Substituting yields dy/dx = -(3x^2 = 5)^-2(6x) = -6x/(3x^2+5)^2

 

[pka]

IF you have copied the problem correctly, then there is a typo in the text.

If u=x<SUP>2</SUP>+5 then du/dx = 2x.

 

[Becky4paws]

Really, really bad...

That's pretty bad alright. This is actually the 'learning example' that the instuctor used in his/her own interpretation of the chapter. I have studied it a hundred times trying to make heads or tails out of "The Chain Rule". Thank goodness you were here....

Guess I'll start studying a different source (LOL). :lol:

 

[pka]

After rereading the first post, it is clear that it should be:
u=3x<SUP>2</SUP>+5, then the text example is correct.