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Differentiate each of the following functions with respect to `x :` (i) `sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2))`(ii) `cos^(-1)(2x(sqrt(1-x^2)),-1/sqrt(2)ltxlt1/sqrt2`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

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  2. Differentiate tan^(-1)((3x-x^3)/(1-3x^2)) , if -1/(sqrt(3))<x<1/(sqrt(...

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  3. Differentiate each of the following functions with respect to x : (...

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

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  5. Differentiate sin^(-1)(2xsqrt(1-x^2))w i t hr e s p e c ttox ,if -1/(...

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  6. Differentiate sin^(-1)(3x-4x^3) with respect to x , if (i)-1/2ltxlt...

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  7. Differentiate cos^(-1)(2x^2-1) with respect to x , if 0<x<1 (ii) -1<x...

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  8. If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)} and 0<x<1, find (dy)/(dx...

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  9. If y=sqrt(a^2-x^2) , prove that y(dy)/(dx)+x=0

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  10. If y=e^x+e^(-x),"p r o v et h a t"(dy)/(dx)=sqrt(y^2-4)

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  11. If y=sqrt(x^2+a^2) ,prove that y(dy)/(dx)-x=0

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

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  13. If y=1/2log((1-cos2x)/(1+cos2x)),p rov et h a t(dy)/(dx)=2cos e c2x

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  14. If y=x e^x, find dy/dx

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  15. If 'y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(...

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  16. If y=sqrt(x)+1/(sqrt(x)),p rov et h a t2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

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  17. P rov et h a t d/(dx){x/2sqrt(a^2-x^2)+(a^2)/2sin^(-1)(x/a) }=sqrt(a^2...

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  18. If x y=4,p rov et h a tx((dy)/(dx)+y^2)=3y

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  19. Differentiate the following functions with respect to x : tan^(-1)s...

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  20. Differentiate the following functions with respect to x : tan^(-1)((...

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