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If y=log{sqrt(x-1)-sqrt(x+1)}, show that...

If `y=log{sqrt(x-1)-sqrt(x+1)},` show that `(dy)/(dx)=(-1)/(2sqrt(x^2-1))`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function 3e^(-3x)"log"(1+x)

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  2. Differentiate the following functions with respect to (x^2+2)/(sqrt...

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  3. If y=log{sqrt(x-1)-sqrt(x+1)}, show that (dy)/(dx)=(-1)/(2sqrt(x^2-1))

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  4. Find (dy)/(dx) in each of the following: 4x+3y="log"(4x-3y)

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  5. Find (dy)/(dx) in each of the following: x^(2/3)+y^(2/3)=a^(2/3)

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  6. Find (dy)/(dx) in each of the following: x y=c^2

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  7. Differentiate the following function with respect to x : cos^(-1){(x+...

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  8. Differentiate the following function with respect to x : sin^(-1){(...

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  9. Differentiate the following function with respect to x : t a n^(-1)...

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  10. Differentiate the following function with respect to x : sin^(-1...

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  11. Differentiate the following function with respect to x : tan^-1(...

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  12. Differentiate the following functions with respect to 3^(x^2+2x

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  13. Differentiate the following function from first principles: e^(3x)

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  14. Differentiate the following functions with respect to 3^(e^x

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  15. Differentiate the following function with respect to x : sin^(-1) {(...

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  16. Differentiate the following functions with respect to sqrt((1-x^2)/...

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  17. Differentiate the following functions with respect to e^(tanx)

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  18. Differentiate the following function sin^(-1)(x/(x^2+a^2))

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  19. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...tooo))), prove that (dy)/(dx)=...

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  20. If y=(sinx)^((sinx)^((sinx)^(...^infty))) , prove that (dy)/(dx)=(y^...

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