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If f(x)=x^(100)+x^(99)+...+x+1, then f^(...

If `f(x)=x^(100)+x^(99)+...+x+1,` then `f^(prime)(1)` is equal to a. 5050 b. 5049 c. 5051 d. 50051

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To solve the problem, we need to find the derivative of the function \( f(x) = x^{100} + x^{99} + \ldots + x + 1 \) and then evaluate it at \( x = 1 \). ### Step-by-Step Solution: 1. **Write the function**: \[ f(x) = x^{100} + x^{99} + x^{98} + \ldots + x + 1 \] ...
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RD SHARMA-DERIVATIVES-Solved Examples And Exercises
  1. Write the value of d/(dx){(x+|x|)|x|}dot

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  2. If f(x)=|x|+|x-1| , write the value of d/(dx)(f(x)).

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  3. Write the value of the derivative of f(x)=|x-1|+|x-3| \ at \ x = 2.

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  4. If f(x)=(x^2)/(|x|), write d/(dx)(f(x))

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  5. Write the value of d/(dx)(log|x|).

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  6. If f(1)=1,f^(prime)(1)=2, then write the value of lim(x->1)(sqrt(f(x))...

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  7. Write the derivative of f(x)=3 \ |2+x| at x=-3.

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  8. If |x|<1 and y=1+x+x^2+x^3+... , then write the value of (dy)/(dx)dot

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  9. Let f(x)=x-[x], x in RR, then f^(prime)(1/2) is a. 3/2 b. 1 c. 0 d. -1

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  10. If f(x)=(x-4)/(2sqrt(x)), then f^(prime)(1) is a. 5/4 b. 4/5 c. 1 d. 0

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  11. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-...

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  12. If f(x)=1-x+x^2-x^3+...-x^(99)+x^(100), then f^(prime)(1) equals a. 15...

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  13. If y=(1+1/(x^2))/(1-1/(x^2)), then (dy)/(dx)= a. -(4x)/((x^2-1)^2) b. ...

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  14. If y=sqrt(x)+1/(sqrt(x)), then (dy)/(dx) \ at \ x=1 is a. 1 b. 1/2 c....

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  15. If f(x)=x^(100)+x^(99)+...+x+1, then f^(prime)(1) is equal to a. 5050...

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  16. If f(x)=1+x+(x^2)/2+...+(x^(100))/(100), then f^(prime)(1) is equal to...

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  17. if y=(sinx+cosx)/(sinx-cosx), then (dy)/(dx) at x=0 is equal to

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  18. If y=(sin(x+9))/(cosx), then (dy)/(dx) at x = 0 is: a. cos9 b. sin9 c...

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  19. If f(x) = (x^n-a^n)/(x-a), then f'(a) is a. 1 b. 1/2 c. 0 d. does not ...

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  20. If f(x) = xsinx, then f'(pi/2) is a. 1/2 b. 1 c. 0 d. -1

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