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If x sqrt ( 1+ y) + y sqrt( 1+x) =0, pro...

If `x sqrt ( 1+ y) + y sqrt( 1+x) =0`, prove that `(dy)/( dx) = - (1)/( (1+x)^2)`.

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ICSE-DIFFERENTIATION-EXERCISE 19 (c )
  1. Differentiate the following w.r.t. x or t or u as the case may be: 2...

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  2. Differentiate the following w.r.t. x : 3x(2x-1) (x+2)

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  3. Differentiate the following w.r.t. x : (x-2) (x+3) (2x +5)

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  4. Differentiate the following w.r.t. x or t or u as the case may be: 5...

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  5. Differentiate the following w.r.t. x : y= (x^2 - 3)/( x+4)

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  6. Differentiate the following w.r.t. x or t or u as the case may be: 7...

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  7. Differentiate the following w.r.t. x or t or u as the case may be: ...

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  8. Differentiate the following w.r.t. x or t or u as the case may be: ...

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  9. Differentiate the following w.r.t. x or t or u as the case may be: 1...

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  10. Differentiate the following w.r.t. x or t or u as the case may be: 1...

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  11. Differentiate the following w.r.t. x or t or u as the case may be: 1...

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  12. If f(x) = (x+2)/( x-2) for all x ne 2, find f' (-2).

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  13. Differentiate (x+2)/(x^2-3) and find the value of the derivative at x ...

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  14. If y= (x)/( x+a), prove that x (dy)/( dx) = y(1-y).

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  15. If x sqrt ( 1+ y) + y sqrt( 1+x) =0, prove that (dy)/( dx) = - (1)/( (...

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  16. Given that y= sqrt( (1-x)/( 1+x)) show that (1-x^(2) ) (dy)/( dx) + y=...

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  17. Given that y= (3x -1)^(2) + (2x -1)^(3), find (dy)/( dx) and the poin...

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  18. (i) If y= (x-1)/( 2x^(2) - 7x +5), find (dy)/( dx) at x=2.

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

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  20. Find the co-ordinates of the points on the curve y= (x)/( 1-x^(2)) " ...

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