Show the rectangular solid of maximum volume inscribed in a sphere is cube Partial Differentiation

PARTIAL DERIVATIVE LINKS Implicit differentiation - Partial derivative - (i) y cos x = x^2+y^2 (ii) e^z = xyz -    • (i) y cos x = x^2+y^2  (ii) e^z = xyz Impl...   Lagrange's Multiplier-Partial derivative-Local Maximum Local Minimum-f(x,y)=x^2+y^2 : 2x+6y=2000 -    • Lagranges Multiplier - Local Maximum Local...   Find the point on the cone closest to the given point - z^2=x^2+y^2 at (4 2 0)-    • Find point on the cone closest to the give...   Find 3 positive numbers with sum 100 and maximum product -    • Find 3 positive numbers with sum 100 and m...   If U = e^xyz Prove that (Ә^3u)/ (ӘxӘyӘz) = (1+3xyz+(x^2)(y^2)(z^2))e^xyz -    • If U = e^xyz  Prove that Ә^3u/ ӘxӘyӘz = (1...   If (x^x)(y^y)(z^z) = c show at x=y=z (Ә^2z)/ (ӘxӘy) = -[x(log ex)]^-1 -    • If x^x y^y z^z = c show at x=y=z  Ә^2x/ӘxӘ...   If u=x^2 tan^-1(y/x) - y^2 tan^-1(x/y) Prove that (Ә^2u)/ (ӘxӘy) = (x^2-y^2)/(x^2+y^2)-    • If u=x^2 tan^-1(y/x) - y^2 tan^-1(x/y) Pro...   If z(x+y)=x^2+y^2 show that (Әz/ Әx - Әz/ Әy)^2 = 4(1- Әz/ Әx - Әz/ Әy)-    • If z(x+y)=x^2+y^2 show that (Әz/ Әx - Әz/ ...   Find the global extrema in two variables f(x)=2x^2+3y^2-12x-6y+9 -    • Find the global extrema in two variables f...   Find the local maxima and minima of x^3-12xy+8y^3 -    • Find the local maxima and minima of x^3-12...   Find the local maxima, minima and saddle points of f(x y)=xy(1-x-y)-    • Find the local maxima minima and saddle po...   Find the local maxima, minima and saddle points of f(x y)=x siny -    • Find the local maxima  minima and saddle p...   Leibnitz Rule - Evaluate ∫(e^(-ax) sin bx)/x dx Hence prove ∫(sinx)/x = П/2 -    • Leibnitz Rule  Evaluate ∫(e^(-ax) sin bx/x...   Leibnitz Rule - Evaluate ∫(e^(-ax) sin x)/x dx = tan^-1(1/a) Hence prove ∫(sinx)/x = П/2 -    • Leibnitz Rule - Evaluate ∫e^(-ax) sin x/x ...   Leibnitz Rule - Evaluate ∫(x(^ α) -1)/log x dx given α greater than 0 -    • Leibnitz Rule - Evaluate ∫(x(^ α) -1)/log ...   Temperature T=400 xyz^2 at point P(x,y,z). Find the highest temperature in unit sphere x^2+y^2+z^2=1 -    • Temperature T=400xyz^2 at point P. Find hi...   Find the maximum and minimum distances of the point (3,4,12) from the sphere x^2+y^2+z^2=1 -    • Find maximum minimum distances of point (3...   Show the rectangular solid of maximum volume inscribed in a sphere is a cube -    • Show the rectangular solid of maximum volu...   Divide 24 in to three parts such that the product of first, square of second, cube of third is maximum -    • Divide 24  to three parts such that  produ...   k=1/2mv^2.Find the change in energy if m and v changes from 40 to 49.5 and 1600 to 1590 respectively -    • k=1/2mv^2 Find change in energy if m v cha...   Calculate the error in area of ellipse if the error in major and minor axis is 1% -    • Calculate  error in area of ellipse if err...   If pv^2=k the relative error in P and V are 0.05 and 0.025. Show that the error in k is 10% -    • If pv^2=k relative error in P  V are 0.05 ...   If radius and height of cone is 4cm and 3cm with error of 0.04 and 0.08cm calculate the percentage error in volume of cone -    • If radius height of cone is 4cm 3cm with e...   Pile of bricks-2m*15m*1.2m. Tape stretches 1%. Count is 450 bricks/cm bricks cost 530/1000 Find approximate error in cost -    • Video   T=2 П(L/g)^1/2 Possible error is 1% in L and 2% in g. Find maximum error in T-    • T=2 П(L/g)^1/2 Possible error  1% in L and...   Error in common logarithm?- error in number 1% -    • Error in common logarithm?- error in numbe...   Find the maximum and minimum values of a function x^3+y^3-3axy=0, a greater 0-   • Find  maximum and minimum values of a func...   Discuss the maxima and minima of the function x^3y^2(1-x-y)-    • Discuss the maxima and minima of the funct...   Rectangular box opened at top volume=32 cubic m. Find least material for construction -    • Partial Differentiation / Rectangular box ...   If u=f(y-z z-x x-y) prove that Әu/Әx + Әu/Әy + Әu/Әz = 0 -    • If u=f(y-z  z-x  x-y) prove that Әu/Әx + Ә...   If u=f(x/y y/z z/x) prove that xӘu/Әx + yӘu/Әy + zӘu/Әz = 0 -    • If u=f(x/y y/z z/x) prove that xӘu/Әx + yӘ...   If z=f(x y) x=e^u+e^-v y=e^-u-v show Әz/Әu - Әz/Әv = xӘu/Әx - yӘu/Әy -    • If z=f(x y) x=e^u+e^-v  y=e^-u-v show Әz/Ә...   If z=f(x y) x=rcosӨ y=rsinӨ Find (Әz/Әx)^2 + (Әz/Әy)^2 -    • If z=f(x y) x=rcosӨ  y=rsinӨ Find (Әz/Әx)^...   If u=x^2+y^2+z^2 x=e^t y=e^tsint z=e^tcost prove that du/dt=4e^t -    • If u=x^2+y^2+z^2  x=e^t y=e^tsint z=e^tcos...   If z=x^2y and x^2+xy+y^2=1 find Әz/Әx -    • If z=x^2y and x^2+xy+y^2=1 find Әz/Әx PART...   If curves f(x y)=0 φ(x y)=0 show at point of contact Әf/Әx Әφ/Әy = Әf/Әy Әφ/Әz Әz/Әx -    • If curves f(x y)=0 φ(x y)=0 show at contac...   RECTANGLE L=x=4 B=y=3 rate of change of x 1.5 y 0.5 find rate of change of area -    • RECTANGLE x=4 y=3 rate of change of x  1.5...   If z=2x^2y-3xy^2 x=3 y=4 dx/dt=2cm/sec find rate of change of y dy/dt -    • If z=2x^2y-3xy^2 x=3 y=4 dx/dt=2cm/sec fin...   Partial differentiaiton If u=x^2+y^2 x=at^2 y=2at find Әu/Әt -    • u=x^2+y^2    x=at^2     y=2at    find Әu/Ә...   Partial differentiaiton If u=f(2x-3y,3y-4z, 4x-2x) prove that (1/2)Әu/Әx + (1/3)Әu/Әy + (1/4)Әu/Әz = 0 -    • u=f(2x-3y 3y-4z 4x-2x) prove (1/2)Әu/Әx + ...   EULERS PARTIAL DERIVATIVE solve u= cosec^-1 [(x^1/2+y^1/2)/(x^1/3+y^1/3)]-    • solve u= cosec^-1 [(x^1/2+y^1/2)/(x^1/3+y^...   EULERS PARTIAL DERIVATIVE solve u= tan^-1 [(x^3+y^3)/(x-y)]-    • solve u= tan^-1 [(x^3+y^3)/(x-y)] EULERS P...