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If 2z=x(2+(dz)/(dx)), then prove that (d...

If `2z=x(2+(dz)/(dx))`, then prove that `(d^(2)z)/(dx^(2))` is a constant.

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SHARAM PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXAMPLE
  1. Differentiate sin^(-1) ((2X)/(1+X^(2))) with respect to cos^(-1) ((1-X...

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  2. Find (dy)/(dx) wheny=x^y.

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  3. If 2z=x(2+(dz)/(dx)), then prove that (d^(2)z)/(dx^(2)) is a constant.

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

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  5. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  6. If (cosx)^(y)=(cosy)^(x), then find (dy)/(dx).

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  7. If x=sqrt(a^(sin^(-1)t)),y=sqrt(a^(cos^(-1)t)), then show that (dy)/(d...

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  8. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t x.

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  9. If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...

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  10. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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  11. If x=a(cost+tsint) and y=a(sint-tcost), then find (d^(2)y)/(dx^(2)) at...

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  12. If x= cos t+ log tan t/2 and y = sin t, then find the value of (d^2y)/...

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  13. If xsqrt(1+y)+ysqrt(1+x)=0 for -1ltx,ylt1 then prove that (dy)/(dx)=(-...

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  14. If x=tan(1/a logy), show that (1+x^2)d^2y/dx^2+(2x-a)dy/dx=0.

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  15. Differentiate the following function w.r.tx tan^(-1)((sqrt(1+x)-sqrt(1...

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  16. If y=sin^(-1)[((5x+12(sqrt(1-x^2)))/13)] then find (dy)/(dx).

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  17. If y=tan(x+y), then find (dy)/(dx).

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  18. If y=x^(cotx)+(sinx)^x then find (dy)/(dx).

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  19. If y=(sin^(-1)x)/(sqrt(1-x^(2))), the prove that (1-x^(2))(d^(2)y)/(dx...

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  20. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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