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Differentiate the following function from first principles: `logcosx`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...tooo))), prove that (dy)/(dx)=...

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

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  3. Differentiate the following function from first principles: logcosx

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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