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If dy/dx=y/x, prove that (d^(2)y)/(dx^(2...

If `dy/dx=y/x`, prove that `(d^(2)y)/(dx^(2))=0`.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-OBJECTIVE TYPE QUESTIONS (VERY SHORT ANSWER TYPE QUESTIONS)
  1. Find the derivative of the following w.r.t. x : 2x+3y=siny

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  2. Find the derivative of the following w.r.t. x : ax+by^(2)=cosy

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  3. Find the derivative of the following w.r.t. x : 1/x-1/y-10=0

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  4. Find the derivative of the following w.r.t. x : y=4/3x^(3//4)

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  5. Find the derivative of the following w.r.t. x : tan^(-1)sqrtx

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  6. Find the derivative of the following w.r.t. x : tan(sin^(-1)x)

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  7. Find the derivative of the following w.r.t. x : xtan^(-1)x

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  8. Find the derivative of the following w.r.t. x : cos^(-1)(e^(x))

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  9. Find the derivative of the following w.r.t. x : log(logx),xgt1

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  10. Find the derivative of the following w.r.t. x : e^(cosx)

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  11. Find (dy)/(dx) , when x=a t^2 and y=2\ a t

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  12. Find dy/dx when x=4t,y=4/t.

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  13. Find (d^(2)y)/(dx^(2)) when y=e^(x)+sinx

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  14. Find (d^(2)y)/(dx^(2)) when y=tan^(-1)x

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  15. Find (d^(2)y)/(dx^(2)) when y=logx/x.

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  16. If dy/dx=y/x, prove that (d^(2)y)/(dx^(2))=0.

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  17. If 2^(x)=3^(y), then find dy/dx.

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  18. Find the second derivative of sin^(-1)x.

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  19. Is Rolle's Theorem applicable to the function: f(x) = |x| in the int...

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  20. Is LMV Theorem applicable to the function: f(x)=sinxsin2x in the int...

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