Question

find the first partial derivatives of z= (2x+3y)^10. the answer is z(x) = 20 (2x +3y)^9. My question is why don't we expand the exponent and then take derivative each part. when considering the whole thing as a function like that, do i miss something? can anyone explain me, please

Answer 1

The method you are suggesting is also correct to the extent that the answer will be same. But of course the process is tedious and time consuming. Also as the exponent increases the method becomes more and more difficult. Hence, this method of chain rule is preferred. You can check it with smaller exponents, say 2 or 3.

Answer 2

Pick me. Pick me!!!

Because that would be insane!!! Do you have a similar plan for an exponent of 3,546,343? How bout an exponent of \(18\sqrt{7}\)?

Answer 3

. @kamalhandoo : thanks a lot. I just want to confirm that both ways are the same answer.
@tkhunny: LOL. it seems you are upset by my stupid question, right? since I am coward and a new comer in Math field, need confirm every thing. Anyway, the way you upset is adorable.Thanks

Answer 4

No, no. No upset at all. It was just crazy. :-)

I do NOT want to discourage you from thinking. Please, feel free to think all the crazy things you wish. If nothing else, this will give you a greater breadth of experience.

Answer 5

ok, I have another question, are you willing to help?

Answer 6

sure go ahead

Answer 7

Let A be a matrix. Show that the matrix AA^T is symmetric. (as short as possible)

Answer 8

Not even a square matrix. Nice. Can you first demonstrate that the product exists?

Answer 9

I copy exactly what the book is. but I think since it has A^T, it must be a square matrix , right? no need to confirm that, right?

Answer 10

I have an idea like : let A = [a(ij)] ---> A^T = [ a(ji)]
then AA^T = [aij] [aji] = a(ii) ---> A A^T is symmetric. is it ...ok? is it weak logic?

Answer 11

No, why does it have to be square?

If A is mxn, and A^T is nxm and A*A^T works to produce mxm. Likewise A^T * A produces nxn.

Hmmm.. If [a(ij)] meant a single value, you might have something, there.

Answer 12

A and A^T must be the same size since A^T is transpose of A, right? and both them must be the square matrix . how a rectangular matrix can have a transpose?

Answer 13

The matrix A doesn't have to be square. When we get a Symmetric Matrix, THAT will have to be square, since B = B^T.

Answer 14

yeah yeah, you are right. i confuse. sorry