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

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

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIATION-Exercise-9(c )
  1. Differentiate f(x) = e^(sin x) w.r.to g(x) = sin x.

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  2. Find the derivative of f (x ) = Tan ^(-1) ((2x )/( 1 - x ^(2))) w.r.t ...

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

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  4. Find the derivative of Tan^(-1)((3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))).

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  5. Simplify each of the following: tan^(-1)(Secx+tanx)

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  6. Write the following function in the simplest form : "tan"^(-1)(sqrt(...

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  7. Find the derivatives of the following function. (logx)^(tanx)

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  8. Find the derivatives of the following function. (x^(x))^(x)=x^(x^(2)...

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  9. Find the derivative of 20^(log(tanx)).

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  10. Find the derivative of the w.r.to x. x ^(x) + e ^(e ^(x))

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  11. Find the derivatives of the following function. x.logx.log(logx)

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  12. Find the derivative of e ^(- ax ^(2)) .sin (x log x ) w.r.t.x

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  13. sin ^(-1) ((2^(x +1))/( 1 + 4 ^(x))) ({:(put), ( 2 ^(x) = tan theta ):...

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  14. Find (dy)/(dx) for the following functions. x=3cos t-2 cos^(3)t, ...

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  15. If x=(3at)/(1+t^(3)),y=(3at^(2))/(1+t^(3)) then find dy/dx.

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  16. Find (dy)/(dx) if x =a ( cos t + t sin t ), y = a ( sin t - t cos t...

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  17. If x=a[(1-t^(2))/(1+t^(2))],y=(2bt)/(1+t^(2) then find dy/dx.

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  18. Differentiate f(x)=log(a)x with respect to g(x)=a^(x).

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

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

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