Home
Class 12
MATHS
If y=(log)e(x/a)^x ,then x^3y2=...

If `y=(log)_e(x/a)^x` ,then `x^3y_2=`

Text Solution

Verified by Experts

`y=(log)_e(x/a)^x`
`y=x(log)_e(x/a)`
`y_1=ln(x/a)+x(1/x)`
`y_1=ln(x/a)+1--(i)`
`y_2=1/x---(ii)`
So,
`x^3y_2`
...
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos
  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

If y=(log)_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=(xy_(1)-y)^(2)(b)(1+y)^(2)(c)((y-xy_(1))/(y_(1)))^(2) (d) none of these

If y=log_(e)((x)/(a+bx))^(x), then x^(3)y_(2)=

If y=log(e^(x^2)) , then dy/dx=?

If y=x^3(log)_e(1+x) , then y'(0) is equal to.......

If y=sin((log)_e x) , then x^2\ (d^2y)/(dx^2)+x(dy)/(dx) is equal to.......

If y=log(e^(-x)+xe^(-x))," then " (1+x)y_(1)=

If y=log((3+e^x)/(3-e^x)) , then dy/dx=?

If y=e^(x+3 log x) , then dy/dx=?

If y=x^(3)log_(e)x, then find y'' andy'''.

RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
  1. If y=tanx+secx ,p rov et h a t(d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

    Text Solution

    |

  2. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

    Text Solution

    |

  3. If y=(log)e(x/a)^x ,then x^3y2=

    Text Solution

    |

  4. If sin^(-1) (1 – x) – 2sin^(-1) x = π / 2,then x is equal to

    Text Solution

    |

  5. If y=2/(sqrt(a^2-b^2)){tan^(-1)((a-b)/(a+b))tanx/2} , then show that (...

    Text Solution

    |

  6. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to -(n-1)^2y (b) (n...

    Text Solution

    |

  7. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

    Text Solution

    |

  8. If x=f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h ...

    Text Solution

    |

  9. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

    Text Solution

    |

  10. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

    Text Solution

    |

  11. If y=tan^-1((log(e/x^2))/(log(ex^2)))+tan^-1((3+2logx)/(1-6logx)), the...

    Text Solution

    |

  12. If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)fx-xy(x)= 1 (b) -1...

    Text Solution

    |

  13. If f(x)=(cosx+isinx)(cos2x+isin2x)(cos3x+isin3x)......(cosn x+isinn x)...

    Text Solution

    |

  14. (d^(20))/(dx^(20))(2cosxcos3x)is equal to (a)2^(20)(cos2x-2^(20)cos3x...

    Text Solution

    |

  15. If x=acosn t-bsinn t ,t h e n(d^2x)/(dt^2) is n^2x (b) -n^2x (c) -n ...

    Text Solution

    |

  16. In (dy)/(dx),x is a independent variable and y is the dependent vari...

    Text Solution

    |

  17. If y^2=a^2cos^2x+b^2sin^2x then prove that (d^2y)/(dx^2)+y=(a^2b^2)/(y...

    Text Solution

    |

  18. If y=sin^(-1)x , show that (d^2y)/(dx^2)=x/((1-x^2)^(3//2))

    Text Solution

    |

  19. If y=Acosn x+Bsinn x , show that (d^2y)/(dx^2)+n^2\ y=0 .

    Text Solution

    |

  20. If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n ...

    Text Solution

    |