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

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

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following function with respect to x : cos^-1s...

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

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

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

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

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  6. If x=sin^(-1)[(2t)/(1+t^2)]'and'y=tan^(-1)((2t)/(1-t^2)), prove that d...

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  7. If x^(13)y^7=(x+y)^(20),p rov et h a t(dy)/(dx)=y/xdot

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  8. Find (dy)/(dx), when x=cos^(-1)1/(sqrt(1+t^2))"and"y=sin^(-1)1/(sqrt(1...

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  9. If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy)/...

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  10. If x=cost " and " y=sint ,"prove : "(dy)/(dx)=1/(sqrt(3))"at " t=(2pi)...

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  11. Differentiate the following functions with respect to cos(logx)hat2

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

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  13. Differentiate the following functions with respect to x : (i)log(c...

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  14. Find (dy)/(dx), y=x^x+x^(1/x)

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  15. Differentiate the following function 3e^(-3x)"log"(1+x)

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

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

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

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

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

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