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If (sinx)^y=(cosy)^x ,p rov et h a t(dy)...

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

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If (sinx)^y=(cosy)^x , prove that (dy)/(dx)=(logcosy-ycotx)/(logsinx+xtany)

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If (cosx)^y=(cosy)^x , find (dy)/(dx)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Find (dy)/(dx), y=((x^2-1)^3(2x-1))/(sqrt((x-3)(4x-1)))

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

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

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

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

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

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

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

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

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

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

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

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  14. Differentiate tan^(-1)((x-1)/(x+1)) with respect to sin^(-1)(3x-4x...

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  15. If y={log(cosx)sinx}"{"log(sinx)cosx")"^(-1)+sin^(-1)((2x)/(1+x^2)), ...

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  16. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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  17. Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(...

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  18. Differentiate sin^(-1)sqrt(1-x^2) with respect to cot^(-1)(x/sqrt(1...

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  19. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

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

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