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If y= 1+ x + (x^2)/( 2!) + (x^3)/( 3!) +...

If `y= 1+ x + (x^2)/( 2!) + (x^3)/( 3!) + (x^4)/(4!) +….` to `oo`, show that `(dy)/( dx) = y`.

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ICSE-DIFFERENTIATION-EXERCISE 19 (b)
  1. Differentiate the following functions: (7)/( x^( (2)/(3) ) )

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  2. Differentiate the following functions: ( sqrt(x) + (1)/( sqrt( x) )...

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  3. Differentiate the following functions: sqrt( x ) - (1)/( sqrt x) , ...

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  4. Differentiate the following functions: 10. (1)/( x) + (3)/( x^2) + ...

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  5. Differentiate the following functions: 11. 2x^((1)/(2)) + 6x^((1)/(3...

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  6. Differentiate the following functions: 12. 8x^(3) - x^(2) + 5 - (2)/...

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  7. Differentiate the following functions: 13. (3 x^7 + x^5 - 2x^4 + x-3...

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  8. Differentiate the following functions: 14. (i) (2x-3)^(2) (ii) (2x -...

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  9. Differentiate the following functions: 15. sqrt ( 3 x +2).

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  10. Differentiate the following functions: Given f(x) = (7)/(4) x^(2), f...

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  11. Find the derivative with respect to x of the following: (i) x - (1)/...

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  12. Find the derivative with respect to x of the following: (ii) sqrt ( ...

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  13. Find the derivative with respect to x of the following: (iii) 3x^(2)...

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  14. Find the derivative with respect to x of the following: (iv) (x^2 + ...

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  15. Find the derivative with respect to x of the following: (2x +x^4)/(...

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  16. Find the derivative with respect to x of the following: (1+x^2)/( x^...

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

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  18. If y= sqrt ( x) + (1)/( sqrtx ), prove that 2x (dy)/( dx ) + y=2 sqrt ...

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  19. If y= (1)/( a-z), show that (dz)/( dy) = (z-a)^(2)

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  20. If y= 1+ x + (x^2)/( 2!) + (x^3)/( 3!) + (x^4)/(4!) +…. to oo, show th...

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