Home
Class 12
MATHS
Differentiate x^x^(2-3)+(x-3)^x^2 with r...

Differentiate `x^x^(2-3)+(x-3)^x^2` with respect to `x` :

Text Solution

AI Generated Solution

To differentiate the function \( y = x^{x^2 - 3} + (x - 3)^{x^2} \) with respect to \( x \), we will follow these steps: ### Step 1: Define the Function Let: \[ y = u + v \] where ...
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.8|6 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Differentiate x^x\ e^(2(x+3)) with respect to x :

Differentiate 5^3-x^2+(3-x^2)^5 with respect to x :

Differentiate x^(cotx)+(2x^2-3)/(x^2+x+2) with respect to x .

Differentiate (2x+5)/(x^(2)-1) with respect to 'x'.

Differentiate sqrt((x+1)(x+2)(x+3)) with respect to x.

Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1/2,1/2)

Differentiate sin^(-1)(3x-4x^3) with respect to x , if -1/2

Differentiate log(3x+2)-x^2log(2x-1) with respect to x :

Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (1/2,\ 1)

Differentiate cos^(-1)(4x^3-3x) with respect to x , if x in (-1,\ -1/2)

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Miscellaneous Exercise
  1. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  2. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

    Text Solution

    |

  3. Prove that:cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-s...

    Text Solution

    |

  4. (log x)^(log x),x gt1

    Text Solution

    |

  5. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

    Text Solution

    |

  6. If y=(sinx-cosx)^(sinx-cosx),pi/4<x<(3pi)/4,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  7. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

    Text Solution

    |

  8. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

    Text Solution

    |

  9. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint)

    Text Solution

    |

  10. If y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , find (dy)/(dx) in each of the ...

    Text Solution

    |

  11. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

  12. "If "(x-a)^(2)+(y-b)^(2)=c^(2), for some cgt0, prove that ([1+((dy)/(d...

    Text Solution

    |

  13. "If "cos y = x cos(a+y)," with "cos a ne pm1," prove that "(dy)/(dx)=(...

    Text Solution

    |

  14. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  15. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  16. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  17. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |

  18. Does there exist a function which is continuous everywhere but not ...

    Text Solution

    |

  19. If y=|f(x)g(x)h(x)l m n a b c| , prove that (dy)/(dx)=|f^(prime)(x)g^(...

    Text Solution

    |

  20. "If "y=e^(a cos^(-1)x),-1lexle1," show that "(1-x^(2))(d^(2)y)/(dx^(2)...

    Text Solution

    |