Home
Class 12
MATHS
Differentiate x^sinx with respect to x :...

Differentiate `x^sinx` with respect to `x` :

Text Solution

Verified by Experts

Let `y=x^(sinx)`
`rArrlogy=log(x^(sinx))`
`=sinxcdotlogx`
`1/y(dy)/(dx)=sinxcdot1/x+logxcdotcosx`
`rArr(dy)/(dx)=y[(sinx)/x+logxcdotcosx]`
`rArr(dy)/(dx)=x^(sinx)[(sinx)/x+logxcdotcosx]cdotAns`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5a|30 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5b|8 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 xsinx with respect to x.

Differentiate e^(sinx) with respect to x :

Differentiate e^(sinx) with respect to x :

Differentiate sinxsiny=x with respect to x

Differentiate sinxtanx with respect to x

Differentiate logsinx with respect to x :

Differentiate sin^3x with respect to x :

Differentiate x^tanx with respect to x :

Differentiate e^(sinx^2) with respect to x :

Differentiate x^(x^x) with respect to x :

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Miscellaneous Exercise
  1. Differentiate x^sinx with respect to x :

    Text Solution

    |

  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. y=(5x)^(3cos 2x) then find (dy)/(dx).

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |