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If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x...

If `y= e^(sin^(-1)x)` and `z=e^(-cos^(-1)x)`, prove that the value of `(dy)/(dz)` independent of x.

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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Short Answer Type Questions)
  1. Differentiate the following functions w.r.t. t : (t^(-2)+t^(2))(2^(...

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  2. Differentiate the following functions w.r.t. t : sqrt(t) e^(t) sec...

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  3. Differentiate the following functions w.r.t. t : (u)/( e^(u) -1)

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  4. Differentiate the following functions w.r.t. t : (u sin u+cos u)/(u...

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  5. If x=a(theta+sin theta) and y=a(1+cos theta), then find the simplified...

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  6. If x=(sin^(3)t)/(sqrt(cos 2t)) and y=(cos^(3)t)/( sqrt(cos 2t)), show...

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  7. Find the differential coefficient of : (tan^(-1)x)/(1+tan^(-1)x)" ...

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  8. Find the differential coefficient of : "tan"^(-1)(sqrt(1+x^(2))-1)/...

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  9. Find the differential coefficient of : "cos"^(-1)(1-x^(2))/(1+x^(2...

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  10. Find the differential coefficient of : x^(sin^(-1)x)" w.r.t. " sin...

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  11. If y=(x)/(sqrt(1+x^(2))), prove that, x^(3)(dy)/(dx)=y^(3).

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  12. If y=e^((y)/(x)) show that, (dy)/(dx)=(y^(2))/(x(y-x)).

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  13. If ye^(y)=x, prove that, (dy)/(dx)=(y)/(x(1+y)).

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

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  15. If y= e^(sin^(-1)x) and z=e^(-cos^(-1)x), prove that the value of (dy...

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  16. If y=sin((pi)/(6)e^(xy)), find (dy)/(dx) at x=0.

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  17. If y=x^(x^(x^(...oo))), then prove that, (dy)/(dx)=(y^(2))/(x(1-y lo...

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  18. If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo), show that, x (dy)/(dx)...

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  19. If y=x+(1)/(x+(1)/(x+…oo)), prove that (dy)/(dx)=(y)/(2y-x).

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  20. Show that the derivative of (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2...

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