Home
Class 12
MATHS
If f,g,a n dh are differentiable funct...

If `f,g,a n dh` are differentiable functions of `xa n d(x)=|fgh(xf)'(xg)'(x h)'(x^(f2)f)' '(x^2g)' '(x^2h)|' prove `
`Delta' =|` (f g h f' g' h' (x^3f'' ')'(x^3g'' ')'(x^3h ' ')'|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

find fogoh If the funtion f(x)=x-1 and g(x)=2x-3, h(x)=4x .

If f: RrarrR and g:RrarrR are two given functions, then prove that 2min.{f(x)-g(x),0}=f(x)-g(x)-|g(x)-f(x)|

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that varphi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x h ' '(x)| is a constant polynomial.

Let f:R to R and h:R to R be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(x))=x for all x in R . Then,

Let f be a twice differentiable function such that f^(primeprime)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11

Let f(x)=x^(2) and g(x)=2x+1 be two real functions. Find (f+g) (x), (f-g) (x), (fg) (x), (f/g) (x) .

f(x)=x^(2)+xg'(1)+g''(2)and g(x)=f(1)x^(2)+xf'(x)+f'(x). The value of g(0) is

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).

If f and g are continuous functions with f(3) = 5 and lim_(xto3)[2f(x)-g(x)]=4 , find g(3).

CENGAGE-DETERMINANTS-All Questions
  1. If (1 + ax + b x^2)^4 = a0 +a1 x + a2 x^2 +...+a8 x^8 when a,b,a0,a1,a...

    Text Solution

    |

  2. Find the value of lambda for which the homogeneous system of equations...

    Text Solution

    |

  3. If f,g,a n dh are differentiable functions of xa n d(x)=|fgh(xf)'(xg...

    Text Solution

    |

  4. If, a,b,c are positive and unequal,show that value of the determinant ...

    Text Solution

    |

  5. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

    Text Solution

    |

  6. Without expanding a determinant at any stage, show that ||x^2+x ,x+1 ,...

    Text Solution

    |

  7. Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^...

    Text Solution

    |

  8. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

    Text Solution

    |

  9. Show that |{:( 2bc-a^2 , c^2 ,b^2),(c^2 , 2ca-b^2 , a^2),(b^2 , a^2 , ...

    Text Solution

    |

  10. If y=|sinxcosxsinxcosx-sinxcosxx1 1|=fin d(dy)/(dx)dot

    Text Solution

    |

  11. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

    Text Solution

    |

  12. Consider the system of linear equations in x , ya n dz : ""(sin3theta...

    Text Solution

    |

  13. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

    Text Solution

    |

  14. If alpha,beta "and" gamma are real number without expanding at any sta...

    Text Solution

    |

  15. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

    Text Solution

    |

  16. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

    Text Solution

    |

  17. Prove that |a1alpha1+b1beta1a1alpha2+b2beta2a1alpha3+b1beta3a2alpha1+b...

    Text Solution

    |

  18. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value...

    Text Solution

    |

  19. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

    Text Solution

    |

  20. If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^...

    Text Solution

    |