Partial derivatives Definition and 435 Threads

In differential geometry what does df mean as in \mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n Then df is what? the jacobian matrix of partial derivatives?

Hello, I'm a student of applied mathematics to economics. Basic course consists of all pure math subjects. We were talking about app's of differentiating the functions u:\mathbb{R}^{n}\to\mathbb{R}^m. We defined a gradient too. In my notes is written: Gravitational potential is a function...

Homework Statement See attatched image. Homework Equations I just don't know where to start... The Attempt at a Solution Any help would be appreciated! :)

Homework Statement 1.if the derivative of f(x,y) with respect to x and y both exist, then f is differentiable at (a,b) 2. if (2,1) is a critical point of f and fxx (2,1)* fyy (2,1) < (fxy (2,1))^2, then f has a saddle point at (1,2) 3. if f(x,y) has two local maxima, then f must have a local...

Hi. So I'm reading a physics book and I come across the following passage: Ok, up to this point I'm fairly confident I'm following along. But then they do the following: and I have no idea where this comes from. I am guessing here that p_i=\phi _i(q) is only in some sufficiently small...

I've been trying to prove that if the following statement holds for all (x,y)ER^2, f must be a linear function: f(x,y)-f(0,0)=x*(d/dx)[f(x,y)]+y*(d/dy)[f(x,y)] It seems to work for any function I plug in, but I'm unable to establish why this always works. Also, when I say (d/dx)[f(x,y)], I...

Homework Statement Let T= g(x,y) be the temperature at the point (x,y) on the ellipse x=2sqrt2 cos(t) and y= sqrt2 sin(t), t is from 0 to 2pi. suppose that partial derivative of T with respect to x is equal to y and partial derivative of T with respect to y is equal to x. Locate the max and...

Homework Statement Determine if the following differential equation is exact. If it is exact solve it. Homework Equations \left(\frac{1}{t} + \frac{1}{t^{2}} - \frac{y}{t^{2} + y^{2}}\right)dt + \left(ye^{y} + \frac{t}{t^{2} + y^{2}}\right)dy = 0 The Attempt at a Solution I am a little...

Homework Statement The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 7 m and w = h = 9 m, and l and w are increasing at a rate of 6 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the following...

Hi everyone! I was wondering if someone could help me with the following question with partial derivatives. A function f: R^2 -> R is defined by f(x,y) = g(x-2y), where g: R-> R. If g'(1)= 3, calculate f subscript x (3,1) and f subscript y of (3,1). thanks!

edit: Totally put this in the wrong forum on accident. Can it be moved to the Calculus and Beyond forum? Thanks. Homework Statement calculate the error associated with stress and strain Homework Equations First equation is stress, second equation is strain. P is load, A is...

Suppose we are given : PV = nRT, where n and R are constants. We are told to find the partial derivative dP/dV. Am I allowed to do this : P = nRT/V Then differentiate this w.r.t. to V. I disregarded the fact that V = 0 makes the RHS undefined. # This question came from...

Hallo, What is the condition for partial derivatives to be continuous (if I have function f(x,y))? Thanks, Omri

Would someone care to explain some basic applications of Partial Derivation in real-world situations? (Note: This is NOT a homework question; it's just a query.)

Homework Statement \int x \frac {\partial f} {\partial x} dx where f=f(x,t) Homework Equations \int u \, dv = uv - \int v \, du The Attempt at a Solution u = x so du = dx and dv = \frac {\partial f} {\partial x} dx so v = \int \frac {\partial f} {\partial x}...

Homework Statement Finding the partial derivative with respect to y, so del(f)/del(y) Homework Equations exp(x+z) - that is e^(x+z) The Attempt at a Solution I firstly thought this was just e^(x+z) but then i realized, shouldn't it be just 0? Since you're finding the partial...

Say you have something like f(x)*(f(y)+f(z)). What are the partial derivatives with respect to each variable? What rules are involved? And how would this differ from f(x)*(g(x)+h(x)).

Homework Statement Show that f(x,y) = -(x^2 - 1)^2 - (yx^2-x-1)^2 has only two critical points, and both are maxima. The Attempt at a Solution Set partial derivatives (wrt x and y) to zero to find critical pts. f_x = -2(x^2 - 1)(2x) - 2(yx^2 - x - 1)(2xy - 1) = 0 f_y = -2(yx^2 - x -...

Hey everybody, first time poster although I've recently come across this forum and it's helped me discover the solution of many problems I've been having. I've seen to come to grips with most partial derivative problems I've come across, however, i still can't get correct solutions to problems...

here is the question: http://i44.tinypic.com/xe53tc.gif here is the solution: http://i43.tinypic.com/2nuokfq.gif my first question regarding this whole thing is. why when the doing the partial derivative by "r" we don't multiply by minus the formula says (minus derivative) but all they do is...

Homework Statement Define f: Rn --------> R as f(x) = (||x||^2)*sin (1/||x||) for ||x|| ≠ 0 f(x) = 0 for ||x|| = 0 Show that f is differentiable everywhere but that the partial derivatives are not continuous. Homework Equations The Attempt at a Solution Showing that it is...

Homework Statement If the equations x^2 - 2(y^2)(s^2)t - 2st^2 = 1 x^2 + 2(y^2)(s^2)t + 5st^2 = 1 define s and t as functions of x and y, find \partial^2 t / \partial y^2 The Attempt at a Solution Equating the two, we get 4y^2*s^2*t = -7s*t^2. My main problem is, as simple as this...

How do you visualize a second order partial derivative with respect to x and then y? fxy or fyx?(same thing, but how to visualize)

Homework Statement Find point closest to origin xy2z3 = 2 Homework Equations The Attempt at a Solution note, k = lagrange multiplier grad f = 2xi + 2yj + 2zk, k grad f = k(y2z3i + 2xyz3j + 3z2xy2k) k = 2xy-2z-3 = x-1z-3 = (2/3)z-1x-1y-2 y = \sqrt{2x^2} x =...

Homework Statement x & y measured in meters. Temperature is T(x,y) Temperatures are noted in table y= 2 4 6 x 4 74 72 68 6 87 80 75 8 90 86 80 Estimate the value of Txy(6,4) & Tu, where u = (i + j)/\sqrt{2} I do no understand how to get the i and...

Hello, I was wondering if I could get some help with a question I have. Homework Statement We are asked to find the first and second order partial derivatives of f(x,y) = x^2 - y^2 - 4x^2/(y - 1)^2 (sorry, I don't know how to write this in latex). I am not really sure how to get started...

Homework Statement Given: \varphi(t) – differentiable function. z=z(x,y) – differentiable function. And there is the following equation: x^2 + y^2 + z^2 = \varphi (ax+by+cz) where a,b,c are constants, Prove that: (cy - bz)\cdot \frac {\partial z}{\partial x} +...

Homework Statement a metal plate is situated in the xy plane and occupies the rectangle 0<x<10 and 0<y<8 where x a y are measure in meters. The temperature oat the pooint x,y on the plate it T(x,y), where T is measured in degrees celcius. note the attached table a- estimate the values...

I am stuck on the question, 'If f is a twice differentiable function of a single variable, find f = z(sqrt(x^2+y^2)) that satisfies d^2z/dx^2 +d^2z/dy^2 = x^2 +y^2 (ALL d's ARE MEANT TO BE PARTIAL DERIVATIVES) i know dz/dx=(dz/du).(du/dx) i can find du/dx but i don't know how to find dz/du

Homework Statement Let u= (x^2 + y^2 + z^2)^\frac {-1} {2} Find \frac {\partial^2 u} {\partial x^2} + \frac {\partial^2 u} {\partial y^2} + \frac {\partial^2 u} {\partial z^2} Homework Equations The Attempt at a Solution \frac {\partial^2 u} {\partial x^2} = -(x^2 + y^2...

Homework Statement w=x^2+y^2+z^2 and ysin(z)+zsinx=0 find (delw/dely)xindpendent find (delw/dellz)zindependent Homework Equations The Attempt at a Solution For the first one I think I can use a chain rule where find (delw/dely)xindpendent= delw/delx*delx/dely +...

Homework Statement x^2+y^2=r^2 y-rcos(pheta) find (partialy/partialr)subscribt phetal, find (partialy/partialpheta)subscribtx, and find (partialy/partial)subsribt pehta Homework Equations im not sure how to write this partial in chain rule form. i think the first one...

Homework Statement Let f = f (u,v) and u = x + y , v = x - y . Assume f to be twice differentiable and compute fxx and fyy f in terms of fu, fv, fuu, fuv fvv. The Attempt at a Solution First off, this is an assignment question. I really do hate cheating, but I need help with this...

Homework Statement If z = 1 / (x^2+y^2-1) show that x(dz/dx)+y(dz/dy)=2z(1+z) 2. The attempt at a solution z = (x^2+y^2-1)^-1 dz/dx = -2x(x^2+y^2-1)^-2 = -2x * z^2 dz/dy = -2y(x^2+y^2-1)^-2 = -2y * z^2 (-2x^2 * z^2) - (2y^2 * z^2) = 2z(1+z) I can express x and y in something like z and x/y...

Homework Statement Let Z = 3x-2y x = u+v ln(u) and y = u^2-v ln(v) Homework Equations find Pdz/Pdu and Pdz/Pdv Pd (partial Derivative) The Attempt at a Solution Pdz/Pdx = 3 Pdz/Pdy = -2 Pdx/Pdu = v/u +1 Pdx/Pdv = ln(u) Pdy/Pdu = 2u Pdy/Pdv = -ln(v)-1...

Homework Statement Find all solutions (x,y) for which fx(x,y) = 0 = fy(x,y) if f(x,y) = 12xy - x^2 y - 2xy^2 Homework Equations The Attempt at a Solution f(x,y)=12xy-x^2y-2xy^2 fx(x,y)=12y-2xy-2y^2 fy(x,y)=12x-x^2-4xy 0=12y-2xy-2y^2 0=12x-x^2-4xy EQ 1: 2xy=12y-2y^2...

Homework Statement suppose that f(x,y)=f(y,x) for all (x,y)\inR^2 show that (for partial derivative ) Df/Dx (a,b)=Df/Dy(b,a) Homework Equations The Attempt at a Solution i don't know how to start can i do like this set g(x,y)=f(y,x) f o g (x,y) =f(x,y) then how to continue ?

Homework Statement if z= f(x) + yg(x), what can you say about zyy explain? Homework Equations The Attempt at a Solution z= f(x,yy) zyy = d/dy (dz/dy) d(partial derivative)

in basic multivariate calculus, i never learned about differentiating functions of multiple variables which are also functions of each other. i.e. \frac{d}{d x_1} \left[ f(x_1, x_2, x_3) \right] where x_1 = g(x_2, x_3) studying thermodynamics right now, I'm encountering into...

Homework Statement (e^0.16)/(1+e^-0.3y) I am suppose to find the fy of this Homework Equations A bit trickier than the last prob i posted The Attempt at a Solution What I did: Since (e^0.16) is a constant, I left it just like that and took the derivative of e(-0.3y) my outcome...

Homework Statement f(x,y)=e^(3x+9y) find fsubxx Homework Equations The Attempt at a Solution I got e^(3x+9y)3, but the stupid web assign won't take it as an answer. I am pretty sure this is the correct answer. Am i wrong? Please help =).

The problem: f(x,y)=-\frac{-7x-2y}{9x+7y} find: fx(x,y) fy(x,y) The attempt: fx(x,y)=\frac{-7-2y}{9+7y} fy(x,y)=\frac{-7x-2}{9x+7} Questions: I'm not exactly sure how to find the partail derivative with a fraction like this one.

Homework Statement Find \frac{\partial z}{\partial u} and \frac{\partial z}{\partial v} using the chain rule. z = \arctan(\frac{x}{y}) , x=u^2+v^2 , y=u^2-v^2 Homework Equations The Attempt at a Solution \frac{\partial z}{\partial u} = \frac{4uv^2}{v^4 - 2u^2v^2 + u^4} *...

Homework Statement First problem: Let f(x,y) = x-y and u = vi+wj. In which direction does the function decrease and increase the most? And what u (all of them) satisfies Duf = 0 Second problem: Let z = f(x,y), where x = 2s+3t and y = 3s-2t. Determine \partial{z^2}/\partial{s^2}...

Is there a general formula for the even partial derivatives of a ratio, where both A and B are functions of f? \frac{\partial ^{(2n)}}{\partial f^{(2n)}} \left( \frac{A}{B} \right) Thanks

Homework Statement We have y' = y^(1/3) with initial condition y(0)=0 It's stated that the partial derivative ∂f/∂y does not exist at y=0. Can anyone explain to me why this is? I don't understand how you can take the partial derivative if its not in the form f(x, y); there...

Homework Statement Use the definition of partial deriviatives as limits to find fx(x,y) and fy(x,y). Homework Equations f(x,y) = \frac{x}{x + y^{2}} The Attempt at a Solution I don't think this is right because I think I should have an answer of 1. fx(x,y) = lim h-> 0...

Hello. Let g(x,y) be a function that has second order partial derivatives. Transform the differential equation \frac{\delta ^{2}g}{\delta x^{2}}-\frac{\delta ^{2}g}{\delta y^{2}}=xyg by chaning to the new variables u=x^2-y^2 and v=xy The equation doesn't have to be solved. Okay, so this is...

Question : g(x,y) = x^3 - 3x^2 + 5xy - 7y^2 Verify that ∇g(0,0) = 0 I looked on wiki and it said the vector of partial derivatives, so my g(x,y) would become ∇g = (3x^2 - 6x + 5y, 5x -14y) so what do i do from here? i don't see what its asking, do i plug x and y as 0 and show I get...

Hey all. I'm having some problems with the partial derivatives of e. I understand the basics such as exy2. where I'm getting confused is with the following dz/dx=e(x+y) and dz/dx=1/ex+ey Can anyone help me out with understanding these??