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If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))...

If `y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e))` , prove that `(dy)/(dx)=e^(x^(e^x)) . x^(e^x){(e^x)/x+e^x.logx}+x^(e^(e^x)).e^(e^x){1/x+e^xdotlogx}+e^(x^(x^e)).x^(x^e).x^(e-1){1+elogx}`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=(sinx)^((sinx)^((sinx)^(...^infty))) , prove that (dy)/(dx)=(y^...

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  2. Differentiate the following function from first principles: logcosx

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  3. If y=e^(x^(e^x))+x^(e^(e^x))+e^(x^(x^e)) , prove that (dy)/(dx)=e^(x^(...

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  4. Find (dy)/(dx), y=e^(3x)sin4x. 2^x

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  5. Differentiate the following function from first principles: e^(sqrt...

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  6. Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sq...

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  7. Differentiate the following functions with respect to (sin^(-1)x^4)...

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  8. Find (dy)/(dx), y=((x^2-1)^3(2x-1))/(sqrt((x-3)(4x-1)))

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

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  10. If (sinx)^y=(cosy)^x ,p rov et h a t(dy)/(dx)=(logcosy-ycotx)/(logsinx...

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  11. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

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  12. If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

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  13. If xsin(a+y)+sina cos(a+y)=0, prove that (dy)/(dx)=sin^2(a+y)/sina

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

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  15. Differentiate the following functions (2^xcosx)/((x^2+3)^2) with res...

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  16. Differentiate the following functions with respect to e^sin^((-1...

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  17. Differentiate the function "sin"(2sin^(-1)x) with respect to x.

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  18. Differentiate the following function sqrt(tan^(-1)(x/2)) with respec...

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  19. Differentiate the following function tan^(-1)(e^x) with respect to...

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  20. Differentiate tan^(-1)((1+a x)/(1-a x)) with respect to sqrt(1+a...

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