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If y=log(sqrt(x)+sqrt(1/x)), prove that ...

If `y=log(sqrt(x)+sqrt(1/x)),` prove that `(dy)/(dx)=(x-1)/(2x(x+1))`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function with respect to x: 10^(logsin...

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  2. If y=logsqrt((1+tanx)/(1-tanx)),"Prove that " (dy)/(dx)=sec2x

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  3. If y=log(sqrt(x)+sqrt(1/x)), prove that (dy)/(dx)=(x-1)/(2x(x+1))

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  4. If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

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  5. Find (dy)/(dx), y=(sinx)^(cosx)+(cosx)^(sinx)

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  6. If y=(x-1)log(x-1)-(x+1)log(x+1), prove : (dy)/(dx)=log((x-1)/(1+x))

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  7. If y=(e^x-e^(-x))/(e^x+e^(-x)) , prove that (dy)/(dx)=1-y^2

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  8. If y=(xsin^(-1)x)/(sqrt(1-x^2)),"p r o v et h a t"(1-x^2)(dy)/(dx)=x+...

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  9. Differentiate the following function tan^2x

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  10. If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)

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  11. If x y^2=1,p rov et h a t2(dy)/(dx)+y^3=0

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  12. Find (dy)/(dx) in each of the following: e^(x-y)=log(x/y)

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  13. Find (dy)/(dx) in each of the following: sinx y+cos(x+y)=1

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  14. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(...

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  15. If ysqrt(1-x^2)+xsqrt(1-y^2)=1," prove that "(dy)/(dx)= - sqrt((1-y^2)...

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  16. Differentiate the following function with respect to x : cos^-1s...

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

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  18. If sec((x+y)/(x-y))=a , prove that (dy)/(dx)=y/x .

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

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

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