Differentiating Definition and 262 Threads

I've been given a couple of problems to do, which I'm unable to because before looking at the question i'd never even HEARD of tanh, which is just... lovely of my lecturer anyway, i had a look around on some websites & fiddled around with it on my calculator and i now have some idea what...

Hey again, well i just studying several vaiable calculus, and encountered the problem of finding the gradient of the scalar field: f = ye^(xy) now I could successfully find the i component (y^2.e^(yx)) but I am having some trouble with the j component. f = ye^{(yx)} if my...

In calculus, my work has recently involved integrating and differentiating the numer e, of which I am very unsure of how to do. I set up some examples for myself to try to figure out, could anyone tell me if they are correct? Please correct me if I am wrong, or tell me where I have made a...

If you differentiate x^2 , you get 2x . But now, if you right x^2 as x+x+x+x+x+x... x times, and then differentiate, you get 1+1+1+1+1+... = x What's wrong. Is it the discontinuity arising from the fact that multiplication can be converted to addition only in integers.

Let y = x^p where p is a natural number. Is it true that \frac{dx^n}{d^ny} = \frac{p!}{(p-n)!} \cdot x^{p-n} with the restriction that we define (-n)! \equiv \infty for n=1,2,3... I found this formula and I believe that it is true if we define (-n)! to equal \infty .

After scanning these post, it is obvious that much of the world is (rightfully) against the war in Iraq and are also anti-american. In your person experience to most people differentiate the actions of the american government from americans in general? I myself being an american am often...

How can this be done? I don't even know how I would begin.. How would you differentiate stuff like x^(y^(x^y))? Where y is a function of x, not a constant of course..

http://www.eden.rutgers.edu/~cjjacob/images/arctan.gif I was given this problem yesterday. It's asking me to differentiate a function containing arctan. Should I find a common denominator and combine them into one term, should I just differentiate each term separately? Please I need help...

For question 3, i don't know ho to differentiate the electromagnetic field. Can someone help me?

Any ideas for solving this, I am having trouble using implicit differentiation along with using log differentiation, thanx!: x^3 + x tan^-1 y = e^y

Hello, My question has to do with differentiating an integral. We are given: f(x)=1/2\int_{0}^{x} (x-t)^2 g(t)dt And we are asked to prove that: f'(x)=x\int_{0}^{x}g(t)dt - \int_{0}^{x}tg(t)dt My Solution: I expanded (x-t)^2 into x^2-2xt+t and then expanded...

Hi all. For any of you who have done differential calculus, I need a little help with a problem involving natural logarithms. The question asks to differentiate y = ln x from first principles . It says "use the definition of the Euler number, namely e = lim(n->inf.) (1+1/n)^n.". First...