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For the function f(x)=(x^(100))/(100)+...

For the function
`f(x)=(x^(100))/(100)+(x^(99))/(99)+….+(x^(2))/(2)+x+1.`
Prove that
`f'(1)=100f'(0)`.

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NCERT BANGLISH-LIMITS AND DERIVATIVES-EXERCISE 13.2
  1. Find the derivative of the following functions from first principle. ...

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  2. Find the derivative of the following functions from first principle. ...

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  3. For the function f(x)=(x^(100))/(100)+(x^(99))/(99)+….+(x^(2))/(2)+x...

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  4. Find the derivative of x^(n)+ax^(n-1)+a^(2)x^(n-2)+…+a^(n-1)x+a^(n) f...

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  5. For some constants a and b, find the derivative of (x-a)(x-b)

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  6. For some constants a and b, find the derivative of (ax^(2)+b)^(2)

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  7. For some constants a and b, find the derivative of (x-a)/(x-b)

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  8. Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a.

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  9. Find the derivative of 2x-(3)/(4)

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  10. Find the derivative of (5x^(3)+3x-1)(x-1)

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  11. Find the derivative of x^(-3)(5+3x)

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  12. Find the derivative of x^(5)(3-6x^(-9))

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  13. Find the derivative of x^(-4)(3-4x^(-5))

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  14. Find the derivative of (2)/(x+1)-(x^(2))/(3x-1)

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  15. Find the derivative of cos (x^3)

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  16. Find the derivative of the following functions: sinxcosx

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  17. Find the derivative of the following functions: sec(x^2+3)

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  18. Find the derivative of the following functions: 5secx+4cosx

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  19. Find the derivative of the following functions: "cosec"(x+2)

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  20. Find the derivative of the following functions: 3cotx+5" cosec "x

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