Differentiating Definition and 270 Threads

I've had troubled sleep because of this...:cry: I tryed a lot and got this... Can you spot any mistakes or give me hints on how to approach this Thanks

i have bee strugglignwith thes ethree questions for some time now done the 1st one like 8 times :S - rewrite each of the following in the form y=u^n or y=ku^n, and then differntiate 1) y = ((1 + x^1/2)/ x^2/3))^3 i started this by doing writing it out as y = [(1+x^1/2)(x^-2/3)]^3 then i...

I have been happilly solving away a multitude of different questions until the book threw me this curve ball...10^(3x) My first attempt was as follows: let y=u^3 and u=10^x dy/du = 3u^2...du/d10 = x(10^(x-1))...3x(10^2x(10^(x-1)))...3x(10^(3x-1)) the answer given in the book however is...

I'm having some trouble differentiating x^{\sqrt x } . I know that the derivative of x^{\sqrt x } probably begins with x^{\sqrt x } \cdot \ln (x) \cdot \frac{1}{{2\sqrt x }} but once the base is also x then there is probably more to it than that. Anyone?

How can I use trig identities to let me differentiate \sin \left ( x + \frac{\pi}{2} \right) and 3 \sin x - 2 \cos x?

[SOLVED] differentiating [ sin(1/ln(x)) / x ].. solution? hello all. I do not have the solution to this question that I am about to ask. But if you find the time, try this solving this problem and feel free to type your answer and compare with mine. differentiate :: sin(1/ln(x)) / x my...

What are the rules for differentiating tan, sin & cos? I know cos = -sin tan = sin/cos?

Hello I have made a simple spline(x,y) of 4 datapoints and I want to differentiate it. I can't get it to work; I have tried fntlr, fnder ect. Can anyone help? Karin

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...