You have a number of options.

As written,

,

is a fraction as so you need the Quotient Rule (http://en.wikipedia.org/wiki/Quotient_rule) to differentiate it.

However, when you are differentiating with respect to , note that the top is a constant…therefore we can write

and differentiate as follows using the Chain Rule:

.

However if you do that you might note that you could have originally written

and used the product rule for differentiating with respect to .

This is a general situation. Suppose you have a function that is a fraction

.

Now you can use the Quotient Rule or else write

and use the Product Rule.

Regards,

J.P.

Just having trouble with the first part of Q.2 on P.65. Do i bring the below the line above and when I do this, do i need a product rule for .

I’m getting an answer of 21!!

Regards.

]]>Firstly I should say that the numbers are ridiculous — errors of 0.1 m would have been more appropriate. Also I have no error in — you interpreted this correctly.

Secondly, when you are differentiating with respect to and , note that because is constant so is .

i.e. you should have

,

and similar for .

Regards,

J.P.

Would you point me in right direction for Q.4?

Thanks.

]]>You are not using the Chain Rule properly.

We have so using the Chain Rule we have

.

Regards,

J.P.

I am having trouble with Q3 part 2 , Could you point me in right direction .

]]>Using a product rule

.

Get back to me if this doesn’t find your problem.

Regards,

J.P.

Just stuck on question 4 – I’m getting a different answer then from the book – am I right in saying we need to use both product rule and chain rule (chain for the ). I have done it both ways still not working.

Regards.

]]>Q.3 (ii)

Everything is correct up until the final line .

Q.6

When you are differentiating with respect to you are keeping constant. Hence is also constant.

Therefore if you are using the product rule you would have

.

…yes your derivative of was incorrect. However, as you can see there is no real need here for the product rule as it is “constant” times “function” and you just need to use

… you pull out the constant.

All you need here is

.

This should make things more straightforward.

Regards,

J.P.

Having trouble with these two questions; would you point me in right direction? ]]>