Home
Class 12
MATHS
Let u(x) and v(x) be differentiable func...

Let `u(x) and v(x)` be differentiable functions such that `(u(x))/(v(x))=7`. If `(u'(x))/(v'(x))=p and ((u'(x))/(v'(x)))=q`, then `(p+q)/(p-q)` has the value of (a) `1` (b) `0` (c) `7` (d) `-7`

A

1

B

0

C

7

D

-7

Text Solution

Verified by Experts

`u(x)=7v(x) or u' (x)=7 v'(x) or p=7" (given)"`
`"Again "(u(x))/(v(x))=7or ((u(x))/(v(x)))=0 or q =0`
`"Now, "(p+q)/(p-q)=(7+0)/(7-0)=1`
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 u and v are two differentiable functions of x show that, (d)/(dx)("tan"^(-1)(u)/(v))=(v (du)/(dx)-u(dv)/(dx))/(u^(2)+v^(2)) .

If u and v are two differentiable functions of x and y = uv , prove that , (y')/(y)=(u')/(u)+(v')/(v) where dash (') denotes derivative w.r.t.x.

Find the differentiation of y=sin u, u=x^2 w.r.t.x.

If (dx)/(dy)=u and (d^(2)x)/(dy^(2))=v , then the value of (d^(2)y)/(dx^(2)) is -

If u and v are two differentiable functions of x and int uv dx=phi(x)-int[(du)/(dx)intv dx]dx , then the value of phi(x) is-

The range of the function " "^(7-x)P_(x-3) is -

Prove that : (v) p^(log_(x)q) = q^(log_(x)p)

Let u=int_0^oo (dx)/(x^4+7x^2+1 and v=int_0^oo (x^2dx)/(x^4+7x^2+1) then find the value of u+v

CENGAGE PUBLICATION-DIFFERENTIATION-Execrises
  1. " If "y=sqrt((1-x)/(1+x))," then "(1-x^(2))(dy)/(dx) is equal to

    Text Solution

    |

  2. If y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se...

    Text Solution

    |

  3. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

    Text Solution

    |

  4. If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to (a...

    Text Solution

    |

  5. Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , wher...

    Text Solution

    |

  6. If underset(trarrx)lim(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 andf(0...

    Text Solution

    |

  7. If f(0)=0,f^(prime)(0)=2, then the derivative of y=f(f(f(x))) at x=0 i...

    Text Solution

    |

  8. If f(x)=sqrt(1+cos^2(x^2)),t h e nf^(prime)((sqrt(pi))/2) is (a) (sqrt...

    Text Solution

    |

  9. d/(dx)cos^(-1)sqrt(cosx)i se q u a lto 1/2sqrt(1+s e cx) (b) sqrt(1+s...

    Text Solution

    |

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

    Text Solution

    |

  11. If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (n y)/(sqrt(x^2+a^2)) (b...

    Text Solution

    |

  12. If y=(log)(sinx)(tanx),t h e n(((dy)/(dx)))(pi/4)i se q u a lto 4/(lo...

    Text Solution

    |

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

    Text Solution

    |

  14. The differential coefficient of f(logex) with respect to x, where f(x)...

    Text Solution

    |

  15. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |