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Find the derivative of x^n + ax^(n-1) + ...

Find the derivative of `x^n + ax^(n-1) + a^2 x^(n-2) + . . .+ a^(n- 1) x + a^n` for some fixed real number a.

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PSEB-LIMITS AND DERIVATIVES-EXERCISE
  1. Find the derivative of the following function from first principle:- (...

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

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

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

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

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

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

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  8. Find the derivative of:- 2x-3/4

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

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

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

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

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

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  14. Find the derivative of cos x from first principle.

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  15. Find the derivative of the following function: sin xcos x

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  16. Find the derivative of the following function: 5secx + 4cosx

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  17. Find the derivative of the following function: cosec x

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  18. Find the derivative of the following function: 3cotx +5 cosecx

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  19. Find the derivative of the following function: 5sinx - 6cosx + 7

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  20. Find the derivative of the following function: 2tanx-7secx

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