# derivation

1. ### Steps of deriving a complicated algebra equation

Hello guys, I am currently working on a physics paper, and in it there is an equation I need to show how to derive. The equation is (it's not in its original form because it has variables containing two letters, and even though one might say it makes no difference, it actually makes the...
2. ### Confused with derivation tree

Hi I am a bit confused by this question could someone please explain to me how I solve this, thanks.
3. ### Calculus derivation of quadric surfaces

Can somebody provide a derivation of the general equations for quadric surfaces, in particular that of a hyperboloid : x^2/a^2 + y^2/b^2 - z^2/c^2 = 1 ? Thanks!
4. ### Derivation of white noise autocovariance function

I am trying to understand the derivation of the white noise autocovariance function (equation 1.12 shown in the image at the bottom). Expanding the covariance function I arrived at: cov(x_s,x_t) = E[(x_s-u_s)(s_t-u_t)] =E[x_s.x_t - x_s.u_t - x_t.u_s + u_s.u_t] =E[x_s.x_t] - E[x_s.u_t] -...

I don't understand the derivation of \tilde{J}_x on page 216 of this (free) book: http://goodfeli.github.io/dlbook/contents/regularization.html According to my calculations, two terms are missing from the 3rd and 4th lines: 2\hat{y}(x)\epsilon^T\nabla_x\hat{y}(x) and...
6. ### Second order implicit partial derivate of x^2y^4+y^7z^8+z^7x^2+5xyz=8

I have been stuck on this problem for a couple of days. I found the first partial derivate of f in regards to x which equals -(2xy^4+2xz^7+5yz)/(8y^7z^7+7y^6x^2+5xy) = -9/20. To find it I used dz/dx=-(dF/dx)/(dF/dz). To find the second derivate I used the quotient rule. The numerator gave me...
7. ### Question about the derivation of fourier series

I try to visualize this in terms of something analogous to vector spaces in linear algebra because thats the only way I can understand the fourier series. You have a basis {$cos(0x), sin(0x), cos(x), sin(x), ...., cos(nx), sin(nx), ...$} and you can represent any function as a linear...
8. ### On the derivation of the line element from scaler quantities

We all know how to derive the differential length elements from the position vector. I was looking at it from a slightly different perspective: ds^2=(x+dx)^2-x^2 + (y+dy)^2-y^2=2xdx+dx^2+2ydy+dy^2 so, how can one show that this is equal to dx^2+dy^2
9. ### derivation formula of variance

can someone show me how to change the circled part?
10. ### Derivation of Taylor series explanatioin

\begin{align*} f^{(k)}(x)&=\sum_{n=k}^\infty n(n-1)(n-2)\cdots(n-k+1)a_nx^{n-k}\cr &=k(k-1)(k-2)\cdots(1)a_k+(k+1)(k)\cdots(2)a_{k+1}x+(k+2)(k+1)\cdots(3)a_{k+2}x^2+\cdots\cr \end{align*}  f^{(k)}(x)=\sum_{n=k}^\infty {n!\over (n-k)!}a_nx^{n-k}= k!a_k+(k+1)!a_{k+1}x+{(k+2)!\over...
11. ### Deriving "left and elimination"

Hey all, been a while since I've visited this site. I have a question that I haven't been able to find the answer to online. given: something and somethingelse [derives] someotherthing we should be able to derive: something, somethingelse [derives] someotherthing Does anyone know how to...
12. ### What is the last step figuring out what to do in this 4th degree formala derivation

I would like to figure out what to do in the next couples steps to finish up the solution. See the attachment: Thank you, Cbarker1
13. ### Energy Balance Equation Derivation

Hi all, I'm looking over some notes at the moment for university and this process has me completely stumped. I've screenshotted a picture of the slide, so hopefully you can all see it ok. Can anyone explain to me how on Earth we go from the 'consider the equation' to the energy balance...
14. ### Derivation of PDF forumula

\frac{P(x_{0} > X > x_{0} + \epsilon)}{\epsilon} \rightarrow f(x_{0}) as \epsilon \rightarrow 0 I'm finding this a bit confusing. I understand that it's supposed to represent that as \epsilon aproaches 0 the probability will be f(x_{0}), I just don't quite understand hwo it's derived...
15. ### function germ and tangential space: show that derivation is zero

Dear mathematicians I don't know if derivation is the right expression but we have the following to solve: Let f,g \in F_p where p is a point of a smooth manifold M. Furthermore assume that f(p)=g(p)=0. Now show that for all v \in T_p M v(fg)=0. According to the lecture we defined F_p to...
16. ### need derivation for creating an elliptical integral form

want to develop an elliptic integral form out of the following integral eqns 1. int(1/(sqrt(1-(k*sin(phi))))) 2. int(sin(phi)/(sqrt(1-(k*sin(phi))))) 3.int(cos(phi)/(sqrt(1-(k*sin(phi)))))
17. ### Partial derivation, Kronecker delta

Hi, i have attached a problem. Can anyone help me???