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Differentiate log{cot(pi/4+x/2)} with re...

Differentiate `log{cot(pi/4+x/2)}` with respect to `x` :

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following functions with respect to (x^2+2)/(sqrt...

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  2. Differentiate x^2(1-x^2) with respect to x .

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  3. Differentiate log{cot(pi/4+x/2)} with respect to x :

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  4. Differentiate the following functions with respect to e^(a x)secxta...

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  5. Differentiate log(cosx^2) with respect to x :

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  6. Differentiate cos(logx)^2 with respect to x :

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  7. Differentiate logsqrt((x-1)/(x+1)) with respect to x :

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

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

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

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

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  12. If y=logsqrt((1-tanx)/(1+tanx)) , prove that (dy)/(dx)=-sec2x .

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

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

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

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  17. If y=e^xcosx , prove that (dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)

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  18. If y=1/2log((1-cos2x)/(1+cos2x)) , prove that (dy)/(dx)=2\ cos e c\ 2x

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  19. If y=x\ sin^(-1)x+sqrt(1-x^2) , prove that (dy)/(dx)=sin^(-1)x

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  20. If y=sqrt(x^2+a^2) , prove that y(dy)/(dx)-x=0

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