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

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