Michael,

Sean is correct but not when he says that the antiderivative of is one. The anti-derivative of doesn’t really make sense but we do have

.

This isn’t even saying that the anti-derivative of is but in fact:

i.e. the anti-derivative of with respect to is … as:

.

See https://jpmccarthymaths.com/2017/02/09/math6037-spring-2017-week-2/#comment-5857 to understand the notation better…

Regarding the anti-derivative of … OK step one says look in the tables and it is the tables…

…

Suppose it wasn’t in the tables… we would have to try a manipulation… so we have:

.

Now I don’t know of any other useful manipulations… and we have no quotient rule so I could try a substitution. For two reasons (it is ‘inside’ the ‘one-over’ and also its derivative is a multiple of ) I pick . This gives

:

.

Now we use the following property of logs that they turn powers into multiplication:

to write

,

by the definition of .

As you can see, it is a good idea that we put it in the tables!!

Regards,

J.P.

OK, using the linear property of differentiation, we can differentiate term-by-term and pull out constants. Recall that with respect to that is a constant:

.

Now the exponential function is defined as the function which is A) equal to its own derivative and B) equal to one at zero. Therefore the exponential function is its own derivative so we have:

.

Regards,

J.P.

Regards.

]]>My bad Mick it is in the tables!!

]]>Mick the anti-derivitive of tanθ is log|secθ|. It’s not in the tables so it’s something you will need to know. The anti-derivitive of dθ is 1 so you just lose that and your left with log|secθ|. That’s my understanding of it anyway.

]]>Sean,

Go to the webpage and go to the Student Resources tab.

The relevant information is in there.

Regards,

J.P.

Do you have a link where we could download maple Please?

Cheers,

Sean

Michael,

No problem.

Email away… I should get back to you tomorrow.

Regards,

J.P.