If u=f(y-z z-x x-y) prove that Әu/Әx + Әu/Әy + Әu/Әz = 0 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 ...
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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 sho...
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) -...
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...
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Leibnitz Rule - Evaluate ∫(e^(-ax) sin x)/x dx = tan^-1(1/a) Hence prove ∫(sinx)/x = П/2 - • Leibnitz Rule - Evalua...
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Rectangular box opened at top volume=32 cubic m. Find least material for construction - • Partial Differentiatio...
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) ...
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) pr...
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...
If z=f(x y) x=rcosӨ y=rsinӨ Find (Әz/Әx)^2 + (Әz/Әy)^2 - • If z=f(x y) x=rcosӨ y...
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^...
If z=x^2y and x^2+xy+y^2=1 find Әz/Әx - • If z=x^2y and x^2+xy+y...
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...
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...
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...
Partial differentiaiton If u=x^2+y^2 x=at^2 y=2at find Әu/Әt - • u=x^2+y^2 x=at^2 ...
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)...
EULERS PARTIAL DERIVATIVE solve u= cosec^-1 [(x^1/2+y^1/2)/(x^1/3+y^1/3)]- • solve u= cosec^-1 [(x^...
EULERS PARTIAL DERIVATIVE solve u= tan^-1 [(x^3+y^3)/(x-y)]- • solve u= tan^-1 [(x^3+...

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