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If f (x) = x-x ^(2) + x ^(3) - x ^(4) +…...

If `f (x) = x-x ^(2) + x ^(3) - x ^(4) +….oo, |x| lt 1,` then `f '(x)=`

A

`(1)/(1 +x )`

B

`(1)/((1+x)^(2))`

C

`(1)/(1-x)`

D

`(1)/((1-x )^(2))`

Text Solution

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The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1A
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  2. If y = log (cos x ) sin x, then , (dy)/(dx ) =

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  3. If f (x) = x-x ^(2) + x ^(3) - x ^(4) +….oo, |x| lt 1, then f '(x)=

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  4. (d)/(dx) {(x +a) (x ^(2) +a ^(2)) (x ^(4)+ a^(4)) (x ^(8) + a^(8))}=

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  5. (d)/(dx) [(x +1)(x^2+1)(x ^(4) + 1) (x ^(8) +1)]=(15 x ^(p) -16x^q+1) ...

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  6. If y = (1 + x) (1 + x^(2)) .. (1 + x^(2n)), then ((dy)/(dx))(x = 0) is...

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  7. If y = log (a) x + log (x ) a + log (x ) x + log (a) a then (dy)/(dx)...

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  8. f (x) = log (e ^(x) ((x-2)/(x +2))^(3//4))impliesf'(0)=

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  9. If y =1 (1)/(1!) + (x ^(2))/(2!)+.. then (dy)/(dx)=

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  10. For |x| lt 1 if 1+ x+x ^(2) … then (dy)/(dx)=

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  11. If |x| lt 1 then (d)/(dx) (1-2x + 3x ^(2) +…)=

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  12. If |x| lt 1 then (d)/(dx) (1+2x+ 3x ^(2) +…)=

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  13. If |x| lt 1 then (d)/(dx ) [1+ (px)/(q) + (p (p+q))/(2 !)((x)/(q))^(2...

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  14. If y = exp {sin ^(2) + sin ^(4) x + sin ^(6) x +…} then (dy)/(dx)=

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  15. (d)/(dx) [x+(x ^(3))/(3 ) + (x ^(5))/(5) +...]=

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  16. (d)/(dx) {cos x ^(0)}=

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  17. The derivative of sin ^(-1) 2x w.r.t x is

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  18. The derivative of Sec ^(-1) 5x w.r.t x is

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  19. The derivative of Tan^(-1) (x//2) w.r.t x is

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  20. The derivative of Cosec ^(-1) (x//3) w.r.t is

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