Home
Class 12
MATHS
"If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((...

`"If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1," prove that "(y')/(y)=(1)/(x)((a)/(a-x)+(b)/(b-x)+(c)/(c-x)).`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

If y=(ax^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1 , then prove that (y')/y=1/x[a/(a-x)+b/(b-x)+c/(c-x)]

If y=(ax^2)/((x-a)(x-b)(x-c))+(b x)/((x-b)(x-c))+c/(x-c)+1 , then prove that (y')/y=1/x[a/(a-x)+b/(b-x)+c/(c-x)]

If (x^(3))/((x-a)(x-b)(x-c))=1 +(A)/(x-a)+(B)/(x-b)+(C)/(x-c) then A=

Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1 = (x^(3))/((x-a)(x-b)(x-c)) .

If (x^(4))/((x-1)(x-2)(x-3))= A.x+B. (1)/((x-1))+C (1)/((x-2))+D. (1)/((x-3))+E , then A+B+C+D+E=

Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1,

Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

If f(x)=((x^2)/(x^b))^(a+b)*((x^b)/(x^c))^(b+c)*((x^c)/(x^a))^(c+a) , then f^(prime)(x) is equal to: (a) 1 (b) 0 (c) x^(a+b+c) (d) None of these

Let a, b, c such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x), a/1+b/3+c/5=

(x^a/x^b)^(a+b).(x^b/x^c)^(b+c).(x^c/x^a)^(c+a)

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g...

    Text Solution

    |

  2. Let f be a continuous, g be a discontinuous function. Prove that f + g...

    Text Solution

    |

  3. Let f(x) be continuous function satisfying the condition f(-x) = f...

    Text Solution

    |

  4. Let R be the set of real numbers and f : R to R be such that for all x...

    Text Solution

    |

  5. The points where the function f(x) = [x] + |1 - x|, -1 < x < 3 where [...

    Text Solution

    |

  6. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

    Text Solution

    |

  7. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

    Text Solution

    |

  8. A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y...

    Text Solution

    |

  9. Given that f(x)= {((1-cos4x)/(x^(2))",","if "x lt 0),(a",","if "x =0),...

    Text Solution

    |

  10. Find (dy)/(dx) at x=-1, when (siny)^(sin.(pix)/(2))+(sqrt3)/(2)sec^(-1...

    Text Solution

    |

  11. Find ("lim")(xvec0){tan(pi/4+x)}^(1//x)

    Text Solution

    |

  12. Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x...

    Text Solution

    |

  13. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

    Text Solution

    |

  14. If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not diff...

    Text Solution

    |

  15. Determine the values of x for which the following functions fails to b...

    Text Solution

    |

  16. "If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1," prove...

    Text Solution

    |

  17. Let alpha in R. Prove that a function f: RtoR is differentiable a...

    Text Solution

    |

  18. Q. f={(x+a if x<0), (|x-1| if x>=0) g(x)={(x+1 if x<0),(x-1)^2 + b ...

    Text Solution

    |

  19. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

    Text Solution

    |

  20. If |cos^-1(1)/(n)|lt (pi)/(2), then lim(n to oo) {(n+1)(2)/(pi)cos^-...

    Text Solution

    |