Question

[sexytrevy]

Hi, this should be easy but i'm just unsure

Comments

[hawkington]

why are you differentiating with respect to the dummy variable t?

[sexytrevy]

Um, I said integrating with respect to t, following that differentiating to x. Is that what you mean?

The question is:
Find the derivatives of the following functions with respect to x: here a is an arbitrary (fixed) real number.

F[x] = t^3 . dt {a -> x^3}

[hawkington]

just integrating with respect to t then differentiating that with respect to x I get 3x^11

What is all this? All you need to do is use the FTC once. You used the FTC wrong, you'll need to review it.

[hawkington]

Hmmm, well FTC is stated differently. There is a corrolary for variable limits of integration, you'll need to review that.

Another route is to write F(x) explicitly in terms of x and a and then to differentiate that with respect to x.

[sexytrevy]

The other route is what I thought I did the second way and ended up with 3x^11...
I'm really not sure what i'm doing wrong, I thought I followed the example exactly...

[hawkington]

You confused me originally. Your work is right. My fault anyways.

There's a corrolary that says the derivative of F(x)=int(f,u(x)->v(x)) is f(v(x))*v'(x)-f(u(x))*u'(x). If you try this you will get the same answer.

[sexytrevy]

Thanx, i'll have a go that way aswell.