Home
Class 12
MATHS
If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^...

If `f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1` is (a)2 (b) 1 (c) `-2` (d) none of these

A

2

B

1

C

-2

D

none of these

Text Solution

Verified by Experts

`y=f(x^(2))`
`"or "(dy)/(dx)=f'(x^(2))2x=2xsqrt(2(x^(2))^(2)-1)`
`"At "=1, (dy)/(dx)=2xx1xxsqrt(2-1)=2`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|29 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|23 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If t a n y=(2^x)/(1+2^(2x+1)),t h e n(dy)/(dx) at x=0 is

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

If y=f((2x-1)/(x^2+1)) and f^'(x)=sinx^2 , then find (dy)/(dx)

If x e^(x y)-y=sin^2x then (dy)/(dx)a tx=0 is a. 0 b. 1 c. -1 d. none of these

If y=f(x^(2)) and f'(x)=sqrt(3x^(2)+1) then the value of (dy)/(dx) at x=2 is -

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equal to 1 (b) 2 (c) 1/2 (d) none of these

If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2 and y(x)=f(e^x)e^(f(x)) , then y^(prime)(0) is equal to a. 1 b. 2 c. 0 d. none of these

If f(x)=int_0^1(dt)/(1+|x-t|) ,then f^(prime)(1/2) is equal to (a)0 (b) 1/2 (c) 1 (d) none of these

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. Evaluate,d/(dx)[sin^2cot^(- 1)sqrt((1-x)/(1+x))] is

    Text Solution

    |

  2. The differential coefficient of f((log)e x) with respect to x , where ...

    Text Solution

    |

  3. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is ...

    Text Solution

    |

  4. If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e ...

    Text Solution

    |

  5. A function f, defined for all positive real numbers, satisfies the equ...

    Text Solution

    |

  6. Let f : (-5,5)rarrR be a differentiable function of with f(4) = 1, f'(...

    Text Solution

    |

  7. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

    Text Solution

    |

  8. If f(x) = x + tan x and f is the inverse of g, then g'(x) is equal to

    Text Solution

    |

  9. If g is the inverse of a function f and f ' ( x ) = 1 / (1 + x^...

    Text Solution

    |

  10. If y = ((sin^ (−1) x)) , prove that ( 1 − x^ 2 ) d 2 y d x 2 − x...

    Text Solution

    |

  11. If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s x/(2y-1)...

    Text Solution

    |

  12. d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b...

    Text Solution

    |

  13. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

    Text Solution

    |

  14. answeer the following : (i) if y sqrt(x^2+1)=log(sqrt(x^2+1)-x), show ...

    Text Solution

    |

  15. "Let "e^(y)=(sqrt(1+alpha)+sqrt(1-alpha))/(sqrt(1+alpha)-sqrt(1-alpha)...

    Text Solution

    |

  16. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

    Text Solution

    |

  17. If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))(1,0) is equal to

    Text Solution

    |

  18. If y=x^((x^(x))) then (dy)/(dx) is

    Text Solution

    |

  19. The first derivative of the function [cos^(-1)(s insqrt((1+x)/2))+x^x]...

    Text Solution

    |

  20. Let f(x)=x^(x),x in (0,oo) and let g(x) be inverse of f(x), then g'(x)...

    Text Solution

    |