Find the partial derivative of the x component of the given function: -x(x2+y2+z2)-3/2

Q: What is y(x) (i.e., y as a function of x) given that dy dx where you are given the boundary…

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Q: Find the derivative of the trigonometric function. g(t) = 3 cos² (πt) g'(t): =

A: Functions are given as and Note:Find:Derivatives of given functions.

Q: Calculate the energy, corrected to first order, of a harmonic oscillator with potential 1 V(x) =kx +…

A: Given, Vx=12kx2+ωx4+ω2x6The 1st excited state wave function for harmonic oscillator potential is…

Q: Suppose that you have the functional J (a) = S². ƒ {y(a, x), y' (a, x); x}dx where y (a, x) = 3x – a…

A: Given, Jα=∫-π2π2fyα,x,y'α,x;xdxyα,x=3x-αcos2xTherefore,y'α,x=3+αsin2x

Q: 1- Find the gradients of the following functions: (a) T =r ( cos0 + sin0 cosØ ). (b) F = e" sin(y)…

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Q: The Duffing oscillator with mass m is described by the non-linear second order DE d? x de + ax + Bx°…

A: An oscillator is described by the non linear second order differential equation : d2xdt2 + αx + βx3…

Q: If Hn (x) is the nth order Hermite polynomial, then which of the following integrals is equal to 0?…

A: Given: Hn(x) is nth order Hermite polynomial.

Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² +…

A: Let the given particle is the electron. Then the transition probability (W) be given as, Where, ω…

Q: Consider the curve described by the parametric equations x = 3 cos t, y = 2 sin t. Compute the slope…

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Q: Let X be a random variable whose density is given by the formula f(x) =  cx2  if    x ∈ (0, 2)…

A: Given: The density is given by,  f(x)=cx2 if x∈0,20 if otherwise Introduction: A random variable is…

Q: Find a scalar potential, fi, if  F=(3x^2yz^2)i+(x^3z^2)j+(2x^3yz)k, and fi(1,1,1)=1

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Q: derivative of the given function keeping E fixed in terms of E and T

A: We have a function n(E)=E2eE/T-1. We need to find its derivative with respect to (a) T keeping E…