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If y = e^(asin^(-1)x) then prove that (d...

If `y = e^(asin^(-1)x)` then prove that `(dy)/(dx) = (ay)/(sqrt(1 - x^2))`

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If y=e^(a sin^(-1)x) then prove that dy/dx=(ay)/(sqrt(1-x^(2)) .

If sqrt(1 - x^(2)) + sqrt(1 - y^(2)) = a(x - y) , then prove that (dy)/(dx) = sqrt((1-y^(2))/(1-x^(2))) .

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

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) then prove that dy/dx=(sqrt(1-y^(2)))/(sqrt(1-x^(2)) .

If x ^(y) = e ^( x -y) , then show that (dy)/(dx) = (log x )/( (1 + log x ) ^(2))

If x ^( log y) = log x, then prove that (dy)/(dx) = (y)/(x) ((1- log x log y)/( (log x) ^(2)))

If x^(y) + y^(x) = a^(b) then prove that (dy)/(dx)=-[(yx^(y-1)+y^(x)Logy)/(x^(y)Logx+xy^(x-1))] .

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If y= Tan^(-1)""(sqrt(1+x^2) -1)/x then (dy)/(dx)=

AAKASH SERIES-DIFFERENTIATION -EXERCISE -4.4
  1. Find the derivatives of the function cot ^(-1) (cosec 3x )

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  2. Find the derivative of y=e^(Sin-1)x.

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  3. Find the derivatives of the function sin ^(-1) sqrtx

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  4. Find the derivatives of the function tan ^(-1) (cos sqrtx)

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  5. Find the derivatives of the function sin (tan ^(-1) (e ^(x)))

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  6. Find the derivatives of the function (cot ^(-1) x ^(3)) ^(2)

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  7. Find the derivatives of the function tan ^(-1) (( cos x )/( 1 + cos ...

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  8. Find the derivatives of the function cos ^(-1) (( b + a cos x )/( a ...

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  9. Find the derivatives of the function log (sin ^(-1) e ^(x))

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  10. Find the derivatives of the function If y = b tan ^(-1)((x )/(a) + ...

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  11. Find the derivative of the function If f(x) = tan ^(-1) ((5 tan ((x...

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  12. Find the derivatives of the function x tan ^(-1) x

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  13. Find the derivative of the function sin x (tan ^(-1) x) ^(2)

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  14. Find the derivative of the function sin ^(2) x (sin ^(-1) x ) ^(2)

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  15. Find the derivatives of the function (x sin ^(-1) x )/( sqrt (1 - x ^...

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  16. Find the derivatives of the function If x = log (1 + sin ^(2)y ) show...

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

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  18. Find the derivatives of the function If x = log (1 + sqrty), then sh...

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  19. If y = e^(asin^(-1)x) then prove that (dy)/(dx) = (ay)/(sqrt(1 - x^2))

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  20. If f(x)=(a^(2)-b^(2))^(-1//2).cos^(-1)((acosx+b)/(a+bcosx)) a gt b gt ...

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