Yes, slightly.

Firstly isn’t a “value”. The -function would be better.

We have, in the first example

.

To say the is cancelled isn’t quite correct. When we write

,

we are looking for all the functions, that when differentiated WITH RESPECT TO , give .

For example,

because when we differentiate with respect to we get:

Note we don’t need the at this point… if you do use it you get:

anyway.

The is only recording what variable we are anti-differentiating with respect to (it has a more concrete meaning when we write — namely the width of the ‘strips’).

Note that you have here and it didn’t cause you a problem…

Now there are a two ways of dealing with this.

Firstly note if then and so

as the derivative of with respect to is one.

Secondly, just like , adding up all the little bits of gives you :

.

Hope this helps.

Regards,

J.P.

Having a little trouble with one part of the questions on p. 31 and p. 32, it’s how you come up with your value?

In Q.1 you anti-differentiate and get and this is fine to me as the is cancelled by the anti differentiation.

But in Q.4 when you anti-differentiate and you come up with as an answer? To me if I am to follow the format of the other questions my answer would have been as the would be cancelled again? Am I looking at this in the wrong way?

Thanks.

]]>David,

Yes, no problem.

Regards,

J.P.

Q. 10: perfect.

Q.4: Usually in calculus\pure maths when we write we mean base :

The calculator takes

,

and you see it behind the button like is behind the button.

To be honest logs base 10 are a relic (http://math.stackexchange.com/questions/552038/are-base-ten-logarithms-relics)

Q.5: This is the Chain Rule (http://en.wikipedia.org/wiki/Chain_rule)

.

In this particular example, there is another way of showing that

.

We have that logs transform multiplication into addition as follows (here the can have any base at all):

.

Applied here we have

.

Now is a constant so its derivative is zero:

.

Regards,

J.P.

Would you a look at my Q.10 and tell me if its solved correctly and I have two queries on Q4 and Q5.

Thanks.

]]>