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Differentiate sin^(-1)sqrt(1-x^2) wi...

Differentiate `sin^(-1)sqrt(1-x^2)` with respect to . if `0

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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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

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  3. Differentiate sin^(-1)sqrt(1-x^2) with respect to . if 0<x<1.

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  4. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),show that" " (x^2+1)(dy)/(dx)+x y+1...

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  5. 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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  6. If y=xsin(a+y),prove that (dy)/(dx)=(sin^2(a+y))/(sin(a+y)-ycos(a+y))d...

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  7. If x ylog(x+y)=1,prove that(dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2+x+y))dot

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  8. If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx

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  9. If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)...

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  10. If (x-y)e^(x/(x-y))=a , prove that (dy)/(dx)+x=2ydot

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  11. Differentiate the following functions with respect to (e^xlogx)/(x^...

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  12. Differentiate the following functions with respect to x log(x+sqrt(...

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  13. Differentiate the following functions with respect to x : tan(e^(s...

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  14. Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"with respect to"x...

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  15. Differentiate the following functions with respect to log((sinx)/(1...

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  16. If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...

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  17. Differentiate the following function sqrt((1+sinx)/(1-sinx))

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  18. If the derivative of tan^(-1)(a+b x) take the value of 1 at x=0,...

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  19. Differentiate the following functions with respect to x e^(3x)cos2x

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  20. If y=sin[2t a n^(-1){sqrt((1-x)/(1+x))}],"f i n d"(dy)/(dx)

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