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if x=e^(t)sin t and y=e^(t)cos t, then p...

if `x=e^(t)sin t` and `y=e^(t)cos t`, then prove that `(x+y)^(2)(d^(2)y)/dx^(2)=2(xdy/dx-y)`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PROBLEM
  1. Test differentiability of the following function at the indicated poin...

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  2. Differentiate x^(sin^(-1)x w.r.t. sin ^(-1).

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  3. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  4. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  5. If 2^(x)+2^(y)+2^(x+y) , then find dy/dx at x=y=1.

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  6. If y=x+e^(x),then find d^(2)x/dy^(2).

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  7. If e^(x)+e^(y)=e(x+y) find dy/dx.

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  8. Differntiate the following functions by proper substitution. [((1+t^2)...

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  9. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  10. Find dy/dx if log sqrt(x^2+y^2)=tan^(-1) (y/x)

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  11. sinx=2t/1+t^(2), tany=2t/1-t^(2), find dy/dx.

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  12. Find dy/dx, x=3 cos t-2cos^3t, y=3sint-2sin^3t.

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  13. If y=sin(mcos^(-1)x) then prove that (1-x^(2))y(2)-xy(1)+m^(2)y=0.

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  14. If y=cos^(-1)((2cosx-3sinx)/sqrt13), then find dy/dx.

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  15. Examine the continuity of the following functions at indicated points....

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  16. Show that f(x)={(x sin frac{1}{x}, xne0),(o,x=0):} is continuous at x...

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  17. Prove that e^x-2=0 has a solution between 0 and 1.

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  18. So that x^5+x+1=0 for some value of x between -1 and 0.

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  19. Examine continuity and differentiability f(x)={[(1-e^(-x))/x,x!=0],[1,...

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  20. If x=2costheta-cos2theta , y= 2sintheta-sin2theta then find d^(2)y/dx^...

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