Home
Class 12
MATHS
If f(x)=|x+a^2a b a c a b x+b^2b c a bb ...

If `f(x)=|x+a^2a b a c a b x+b^2b c a bb c x+c^2|,fin df^(prime)(x)dot`

Text Solution

Verified by Experts

`f(x)=[[x^{2}+a^{2} , a b, a c],[ a b ,x+b^{2}, b c],[ a b , b c , x+c^{2}]]`
`f(x)=[(x^{2}+a^{2})(x+b^{2})(x+c^{2})+2 a^{2} b^{2} c^{2}]`
`=[a^{2} b c(x+b^{2}) g+b^{2} c^{2}(x+a^{2}) +a^{2} b^{2}(x+c^{2})]` ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

If f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2|,t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot

If a , b , c are real numbers, then find the intervals in which f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2| is increasing or decreasing.

The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a. |b x+a y c x+b y b^(prime)x+a ' y c^(prime)x+b ' y| b. |a x+b y b x+c y a^(prime)x+b ' y b ' x+c ' y| c. |b x+c y a x+b y b^(prime)x+c ' y a^(prime)x+b ' y| d. |a x+b y b x+c y a^(prime)x+b ' y b^(prime)x+c ' y|

The value ((x^a)/(x^b))^((a^2 + ab + b^2)) ((x^b)/(x^c))^((b^2 + bc + c^2))((x^c)/(x^a))^((c^2 + ca + a^2)) is :

If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x) for which F(c) is a maximum, f^(prime)(c) is given by a. f^(prime)(c)=(f(b)-f(a))/(b-1) b. \ f^(prime)(c)=(f(b)-f(a))/(a-b) c. f^(prime)(c)=(2(f(b)-f(a)))/(b-a) d. f^(prime)(c)=0

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate sin^(-1)(2a xsqrt(1-a^2x^2)) with respect to sqrt(1-a^2x...

    Text Solution

    |

  2. Differentiate tan^(-1)((1-x)/(1+x)) with respect to sqrt(1-x^2) , if -...

    Text Solution

    |

  3. If f(x)=|x+a^2a b a c a b x+b^2b c a bb c x+c^2|,fin df^(prime)(x)dot

    Text Solution

    |

  4. If fr(x),gr(x),hr(x),r=1,2,3 are polynomials such that fr(a)=gr(a)=hr...

    Text Solution

    |

  5. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

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

    Text Solution

    |

  7. If y =| [f(x) , g(x) , h(x)], [l , m , n], [a , b , c] | , prove tha...

    Text Solution

    |

  8. If f(x)=(log)e((log)e x) , then write the value of f^(prime)(e) .

    Text Solution

    |

  9. If f(x)=x+1 , then write the value of d/(dx)(fof)(x) .

    Text Solution

    |

  10. If f^(prime)(1)=2 and y=f((log)e x) , find (dy)/(dx) at x=e .

    Text Solution

    |

  11. If f(1)=4 , f^(prime)(1)=2 , find the value of the derivative of lo...

    Text Solution

    |

  12. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...

    Text Solution

    |

  13. Let g(x) be the inverse of an invertible function f(x) which is deri...

    Text Solution

    |

  14. If y=sin^(-1)(sinx) , -pi/2llexlepi/2 . Then, write the value of (dy...

    Text Solution

    |

  15. If pi/2lt=xlt=(3pi)/2 and y=sin^(-1)(sinx) , find (dy)/(dx) .

    Text Solution

    |

  16. If pilt=xlt=2pi and y=cos^(-1)(cosx) , find (dy)/(dx) .

    Text Solution

    |

  17. If y=sin^(-1)((2x)/(1+x^2)) , write the value of (dy)/(dx) for x >1 .

    Text Solution

    |

  18. If f(0)=f(1)=0 , f^(prime)(1)=f^(prime)(0)=2 and y=f(e^x)e^(f(x)) , wr...

    Text Solution

    |

  19. If y=x|x| , find (dy)/(dx) for x<0 .

    Text Solution

    |

  20. If y=sin^(-1)x+cos^(-1)x ,\ find (dy)/(dx) .

    Text Solution

    |