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Let f , g : (a,b) rarrR be differentiabl...

Let f , g : `(a,b) rarrR` be differentiable functions. Show that d(fg) = fdg + gdf.

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fdg+gdf
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FULL MARKS-DIFFERENTIALS AND PARTIAL DERIVATIVES -Additional Questions Solved
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  2. Using differentials, find the approximate value of each of the followi...

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  3. Using differentials, find the approximate value of each of the followi...

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  4. Find approximate value of f (5.001) where f(x) =x^3-7x^2+15 .

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  5. If the radius of a sphere , is measured as 7m with an error of 0.02 m ...

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  6. Find the differential dy and evaluate dy for the given values of x an...

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  7. The edge of a cube was found to be 30 cm with a possible error in meas...

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  8. The radius of a circular disc is given as 24 cm with a maximum error i...

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  9. If u = log (tan x + tan y + tanz) , prove that sum sin 2x (delu)/(de...

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  10. If U = (x-y) (y-z) (z-x) then show that Ux+Uy+Uz = 0

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  11. If u=x^2+3xy+y^2 Verify (del^2u)/(delxdely)=(del^2u)/(delydelx).

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  12. If u = x/y^2- y/x^2 , show that (del^2u)/(delxdely)=(del^2u)/(delydelx...

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  13. Suppose that z=ye^(x^2) where x = 2t and y = 1 then find (dz)/(dt)

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  14. If w=x+2y+z^2and x= cos t , y = sin t, z = t Find (dw)/(dt) .

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  15. If f(x,y) = 1/(sqrt(x^2+y^2)) then show that x(delf)/(delx)+y(delf)/...

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  16. Using Euler's theorem , prove that x(delu)/(delx)+y(delu)/(dely)=1/2ta...

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  17. If u= x^y then is equal to ..........

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  18. If u= sin^(-1)((x^(4) + y^(4))/(x^(2) + y^(2))) and f= sin u then f is...

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  19. If u=1/(sqrt(x^2+y^2)) , then x(delu)/(delx)+y(delu)/(dely) is equal t...

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  20. The curve y^2(x-2)=x^2(1+x) has .......

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  21. If x= r cos theta, y = r sin theta, then (del r)/(del x)=

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