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If y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x...

If `y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)}` and 0

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`y=cos^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)}`
`y=pi/2-sin^(-1){xsqrt(1-x)+sqrt(x)sqrt(1-x^2)}`
`y=pi/2-sin^(-1){xsqrt(1-(sqrt(x))^2)+sqrt(x)sqrt(1-x^2)}`
`y=pi/2-sin^(-1){xsqrt(1-y^2)+ysqrt(1-x^2)}`
=`pi/2-(sin^(-1)x+sin^(-1)sqrt(x))`
=`cos^(-1)x-sin^(-1)sqrt(x)`
`dy/dx=-1/sqrt(1-x^2)-1/(2sqrt(x)sqrt(1-x))`
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate sin^(-1)(3x-4x^3)

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

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

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

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

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

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

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

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  9. If y=e^xcosx ,p rov et h a t(dy)/(dx)=sqrt(2)e^xcos(x+pi/4)

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  10. If y=(x-1)log(x-1)-(x+1)log(x+1),p rov et h a t(dy)/(dx)=log((x-1)/(1+...

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

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

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

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

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

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  16. Differentiate the following functions with respect to x : tan^(-1)((3...

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

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

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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){s...

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