Partial differentiation Definition and 126 Threads

Homework Statement Find the partial of z with respect to x keeping r constant. Homework Equations z=x2+y2 x= rcos(t) y= rsin(t) The Attempt at a Solution= r^2(cos(t))^2 + r^2(sin(t))^2 use product rule on "x" and hold r and y constant = [0(cos(t))^2 + r^2(2cos(t))(-sin(t)))] + 0...

g = GM/r^2.. since g is an acceleration, Can g be written like this?...g = dv/dt differentiation of velocity..Or partial derivative ∂v/∂t...is this correct...wat is the difference between differentiation and partial differentiation..can somebody explain me which is correct...

Do you guys know if it's possible to solve for the following integral l(t)=∫ {a+ [b+cL(t)+exp^L(t)]/d } dt where a, b, c and d are constants and the derivative of L(t) is l(t). Thanks in advance!

I know I should know this... it looks so ridiculously easy. In the course of getting d'Alembert's wave equation solution, we get the following equation: 2cp'\left(x\right)=cf'\left(x\right)+g\left(x\right) The primes are derivatives wrt t. Then we re-order the equation and "integrate the...

Homework Statement Find the general solution of y' + (2/x)y = 3/(x^2) The Attempt at a Solution xy' + 2y = 3/x d/dx (x * 2y) = 3/x integrating both sides (using product rule for LHS) I end up with y= (3lnx + C)/2x Then I am supposed to find the solution for which y(2)...

Homework Statement Differentiate f = arctan(u/v) with respect to u The Attempt at a Solution Using the chain rule fu = (1/(1 + (u/v)2)) * 1/v = 1/(v + u2/v) The solutions manual says v/(u2 + v2) What is my mistake?

f(x,y)=2e^(x^2y), then fx(0,1) = ? fx = 4xye^(x^2y) =4(0)(1)e^(0)(1) =e^0 =1? I'm told that I'm getting this question wrong but don't know how. Can anybody please help show me what I'm doing wrong on this one?

Ok here goes... z=x^{2}+y^{2} x=rcos\vartheta y=r sin\vartheta Find: \[ \frac{\partial z}{\partial x}_{y}, \[ \frac{\partial z}{\partial \vartheta}_{x}, \[ \frac{\partial z}{\partial r}_{y}, \[ \frac{\partial z}{\partial r}_{ \vartheta}...

Hello guys, My class is heading into energy with non-conservative and conservative forces. I am not in Calc this semester so is there a guide to partial differentiation and gradients that you can share with me to get up to speed? Thanks

Homework Statement Suppose that Alpha AS and Beta AS manufacture competitive products, with the weekly sales of each product determined by the selling price of that product and the price of its competition. Suppose that Alpha sets a sales price of x dollars per unit for its product, while...

Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?

Hi guys, I have the following question for a uni assignment, I have done part A and found the stationary points to be at x=-2 x = 2 y=-1 y=1 Not sure if it is correct though. I did this by using finding the partial derivatives using the quoitent rule, then making the partial...

The title should have been partial differential equations. PDEs are solved usually by separation of variables but that assumes each solution is a product of two functions which are only dependent on one variable only. But could there exist solutions which are not in the this form? If so how...

This is supposed to be year1 calculus question but I can't answer it. If f:R_2-->R is 0 if (x,y)=(0,0) and xy(x_2-y_2)/(x_2+y_2) otherwise then evaluate 2nd order partial derivative DxDyf(0,0) and Dy,Dxf(0,0) The thing is, I get some complicated looking expression for DxDyf(x,y) and I can't...

given f=ln(x^3+y^3+z^3-3xyz)To prove df/dx+df/dy+df/dz=3/(x+y+z) also finding (d^2/dx^2+...similar two more terms)f=? d => del & (d^2/dx^2+...)^2f=? I have done the first part of the problem.The trick is to write e^f=x^3+y^3+z^3-3xyz and then to differentiate...

Hi to all, I have been given the following problem as an assignment. \frac{\partial ^2 \phi}{\partial \rho^2} + \frac{1}{\rho}\frac{\partial \phi}{\partial \rho} + \frac{1}{\rho^2}\frac{\partial \phi}{\partial \chi^2} + \frac{\partial ^2 \phi}{\partial Z^2}+B^2\phi = 0 Here is my...

Say, E is dependent to x,y,z. I'm expecting it's derivative at x_0,y_0,z_0 to be dE = \lim_{\substack{\Delta x\rightarrow 0\\\Delta y\rightarrow 0\\\Delta z\rightarrow 0}} E(x_0+\Delta x, y_0+\Delta y,z_0+\Delta z) - E(x_0,y_0,z_0) But with following definition, it's not the thing above: dE...

i ve never read partial DE...nd i don't kno how to do this question i got in homework...pleasez help (x^2+y^2+z^2)^-1/2=V prove dv^2/dx^2 + dv^2/dy^2 + dv^2/dz^2 = 0 (i wrote "d" for partial differential) i know its a basic question but i can't understand the technique

Partial Differentiation help please! Hi, I was wondering if anyone is doing degree level maths who can help me with the following question. Thanks very much! I was asked to find the first partial derivatives of z (in terms of x and y) with respect to x and y where: z = e^(uv) where u = x...

Hi, can anyone help me with the following differentiation question? Find first partial derivatives w.r.t to x and y for: tan (x/y) Can anyone offer any help on how to approach this question? I know when you differentiate (x/y) using the product rule, that you have to differentiate y...

If there is such a thing. I need to find \partial z / \partial x given x + y + z = \cosh xyz. I've never seen the likes of this before and I haven't a clue where to start. Would a reasonable start be to take \partial /\partial x of both sides? If so, it seems like I'm going to end up with an...

hi all! I know how to solve the part (i) but not part (ii). Could anyone help?

Hi, this is a pretty trivial question. would be grateful if someone could answer it for me. in spherical polars x=rcos(theta)sin(PHI) and so on for y, and z Now, why is d/dr= dx/dr*d/dx + dy/dr*d/dy+ dz/dr*d/dz where everything is partial. dx/dr, dy/dr and dz/dr at partial...

If z = f(x,y), where x = rcos(\theta) and y = rsin(\theta), find \frac{\partial z}{\partial r}, \frac{\partial z}{\partial\theta}, and \frac{\partial^2 z}{\partial r\partial\theta} Here's what I've done: (a) \frac{\partial z}{\partial r} = \frac{dz}{dx} \frac{\partial x}{\partial r} +...

I know complex total differentiation is defined in analytic function theory. df = f'(z) dz z = x + iy, dz = dx + idy Is there complex partial differentiation? Given a real value function F(z^*, z, t) How would you define \partial F\over\partial z \partial F\over\partial z^* ?

Maths Question: I am having a lot of problems with this question, can any undergrad physicists or mathematicians help me? (note: p before a differntial= partial derivative) . Spherical polar coordinates (r, (thetha), (phi)) are defined in terms of Cartesian coorindates (x,y,z) by...