Home
Class 12
MATHS
d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equ...

`d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}]` equals
`(a) (x^2-1)/(x^2-4)`
(b) 1
(c) `(x^2+1)/(x^2-4)`
(d) `e^x(x^2-1)/(x^2-4)`

A

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

B

1

C

`(x^(2) + 1)/(x^(2)-4)`

D

`e^(x). (x^(2) -1)/(x^(2)- 4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.1|34 Videos
  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.2|10 Videos
  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5o|20 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If y=log((x^(2))/(e^(2))) then (d^(2)y)/(dx^(2)) equal to: a) -(1)/(x) b) -(1)/(x^(2)) c) (2)/(x^(2)) d) -(2)/(x^(2))

int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a) 1/2(ln((x-1)/(x+1)))^2+C (b) 1/2(ln((x+1)/(x-1)))^2+C (c) 1/4(ln((x-1)/(x+1)))^2+C (d) 1/4(ln((x+1)/(x-1)))^2+C

(d)/(dx)(e^((1)/(2)log(1+tan^(2)x))) is equal to

int(x dx)/((x-1)(x-2) equal(A) log|((x-1)^2)/(x-2)|+C (B) log|((x-2)^2)/(x-1)|+C (C) log|((x-1)^2)/(x-2)|+C (D) log|(x-1)(x-2)|+C

intx^(3) log x dx is equal to A) (x^(4) log x )/( 4) + C B) (x^(4))/( 8) ( log x - ( 4)/( x^(2)))+C C) (x^(4))/( 16) ( 4 log x -1) +C D) (x^(4))/( 16) ( 4 log x +1) + C

If y=tan^(-1){((log)_e(e//x^2))/((log)_e(e x^2))}+tan^(-1)((3+2\ (log)_e x)/(1-6\ (log)_e x)) , then (d^2y)/(dx^2)= (a) 2 (b) 1 (c) 0 (d) -1

Find y(x) , if it satisfies the following differential equation (dy)/(dx)=(x-y)^2 , and given that y(1)=1 (A) -ln|(1-x+y)/(1+x-y)|=2(x-1) (B) ln|(2-y)/(2-x)=x+y-1 (C) ln|(1-x+y)/(1+x-y)|=2(x-1) (D) 1/2ln|(1-x+y)/(1+x-y)|+ln|x|=0

intsqrt((e^x+1)/(e^x-1))dx (A) ln (e^(x)+sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (B) ln(e^(x)+sqrt(e^(2x)-1))+sec^(-1)(e^(x))+C (C) ln (e^(x)-sqrt(e^(2x)-1))-sec^(-1)(e^(x)) +C (D) ln(e^(x)+sqrt(e^(2x)-1))-sin^(-1)(e^(-x))+C

Differentiate log((x^2+x+1)/(x^2-x+1)) with respect to x .

Let f(t)="ln"(t) . Then, (d)/(dx)(int_(x^(2))^(x^(3))f(t)" dt")

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Exercies 5p
  1. f (x) = {{:((|x^(2)- x|)/(x^(2) - x),xne 0"," 1),(1",", x = 0),(-1","...

    Text Solution

    |

  2. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

    Text Solution

    |

  3. The points of discontinuity of the function f (x) = {{:(3x + 1"," ,...

    Text Solution

    |

  4. If f (x) = sin (x)/(x), x ne 0 then the value of the function at x = ...

    Text Solution

    |

  5. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

    Text Solution

    |

  6. If (x) = |x| + |x - 1|, than :

    Text Solution

    |

  7. Given that f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),(...

    Text Solution

    |

  8. If f (x) {{:((1 - cos 8 x )/(x^(2)) "," x ge 0 ),(lambda ", ...

    Text Solution

    |

  9. The function f(x)={x} , where [x] denotes the greatest integer functio...

    Text Solution

    |

  10. If f(x)=(2x+3sinx)/(3x+2sinx) , x!=0 is continuous at x=0 , then find ...

    Text Solution

    |

  11. If f(x)=sin^(-1) ((2x)/(1+x^2)) then f(x) is differentiable on

    Text Solution

    |

  12. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

    Text Solution

    |

  13. d/(dx)[log{e^x((x-2)/(x+2))^(3//4)}] equals (a) (x^2-1)/(x^2-4) (b...

    Text Solution

    |

  14. If x=acos^(3) theta, y=a sin^(3) theta, then ([1+((dy)/(dx))^(2)]^(3//...

    Text Solution

    |

  15. If f (x) = tan ^(-1)sqrt((1 + sin x )/(1 - sin x)), 0 le x le (pi)/(2)...

    Text Solution

    |

  16. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 ...

    Text Solution

    |

  17. If y^(2) = ax^(2) + bx + c where a, b c are contants then y^(3)(d^(2...

    Text Solution

    |

  18. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...

    Text Solution

    |

  19. "If "y^(1//m)=(x+sqrt(1+x^(2)))," then "(1+x^(2))y(2)+xy(1) is (where ...

    Text Solution

    |

  20. If y = sin ^(2) alpha + cos ^(2) (alpha + beta) + 2 sin alpha sin beta...

    Text Solution

    |