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Find the derivative of f (x) w.r.t. g(x)...

Find the derivative of `f (x)` w.r.t. g(x) for the
`f (x) = Tan ^(-1) ((sqrt (1 + x ^(2)) -1)/( x )), g (x) = Tan ^(-1) x`

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The correct Answer is:
`(1)/(2)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. Differentiate f(x)=log(a)x with respect to g(x)=a^(x).

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  2. Differentiate f(x) with respect to g(x) for the following . f(x)=sec...

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  3. Find the derivative of f (x) w.r.t. g(x) for the f (x) = Tan ^(-1) (...

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  4. Find the derivative of x^(4)+y^(4)-a^(2)xy=0.

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  5. Find the derivative of y=x^(y).

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  6. Find the derivative of the function y defined implicitly by each of th...

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

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  8. If y=xsqrt(a^(2)+x^(2))+a^(2)log(x+sqrt(a^(2)+x^(2))), then show that ...

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  9. If x^(logy)=logx then find dy/dx.

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  10. If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(...

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  11. If x^(y)=y^(x) then show that dy/dx=(y(xlogy-y))/(x(ylogx-x)).

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  12. If x ^(3) + y ^(3) =3 axy then (dy)/(dx) =

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  13. Find the derivative dy/dx of the function y=((1-2x)^(2//3)(1+3x)^(-3//...

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  14. Find the derivative (dy)/(dx) of each of the following functions. y=...

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  15. Find (dy)/(dx) for the function (using logarithms). y = ((a - x ) ^(...

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  16. Find (dy)/(dx) for the function (using logarithms). y = (x ^(3) sqrt...

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  17. Differentiate sqrt(((x-3)(x^(2)+4))/((3x^(2)+4x+5))).

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  18. Find the derivative of (sinx)^(log x)+x^(sinx).

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  19. Find the derivatives of the following functions. x^(x^(x))

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  20. Find the derivative of (ii) (sinx)^(x)+x^(sinx) w.r.to x.

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