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Differentiate the following functions wi...

Differentiate the following functions with respect to `x :` `(cos"x")^x` (ii) `x^(sqrt(x))` `(log"x")^(sinx)` (iv) `(sinx)^(cosx)`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate: (logx)^x+x^(logx)w i t hr e s p e c t to x :

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  2. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3)) with respec...

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  3. Differentiate the following functions with respect to x : (cos"x")^x ...

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  4. Differentiate the following functions with respect to x : (i) (x^x...

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

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

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  7. If y=cos^(-1)sqrt((cos3x)/(cos^3x)),t h e ns howt h a t(dy)/(dx)=sqrt...

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  8. If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y),p rov et h a t(dy)/(dx)=sqrt((1-y^2...

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  9. if x^2+y^2 = t - 1/t and x^4 + y^4 = t^2 + 1/t^2 then prove that dy/dx...

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  10. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

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  11. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  12. Differentiate sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-x^2)/(1+x^2)) with re...

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  13. Differentiate the functions with respect to x : tan^(-1){(sqrt(1+a^2x...

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  14. Differentiate the functions with respect to x : cos^(-1){(cosx+sinx...

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  15. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

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  16. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

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

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  18. If y = cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2), -1/2ltxlt0 , find (dy)/(dx...

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  19. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),p rov et h a t(dy)/(dx)=(x^2)/(y...

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  20. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

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