Home
Class 12
MATHS
Differentiate (sin^(-1)x^4)^4 with respe...

Differentiate `(sin^(-1)x^4)^4` with respect to `x` :

Text Solution

Verified by Experts

Let `y=(sin^(-1)x^4)^4`
so, `(dy)/(dx)=d/(dx)((sin^(-1)x^4)^4)`
`=4(sin^(-1)x^4)^3 xx d/(dx) (sin^-1 x^4)`
`=(4(sin^(-1)x^4)^3 )/sqrt(1-x^8) xx d/(dx) (x^4)`
`=(16x^3 (sin^(-1)x^4)^3 )/sqrt(1-x^8)`
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

Differentiate (sin^(-1)x)^(x) with respect to x:

Differentiate sin(m sin^(-1)x) with respect to x

Differentiate sin(2sin^(-1)x) with respect to x

Differentiate sin^(-1)(x^(3)) with respect to x:

Differentiate (a^(sin^(-1)x))^(2) with respect to x:

Differentiate x^(sin^(-1)x) with respect to sin^(-1)x

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

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

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

Differentiate cos^(-1)(sin x) with respect to x:

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. Differentiate (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)) with...

    Text Solution

    |

  2. Differentiate log{x+2+sqrt(x^2+4x+1)} with respect to x :

    Text Solution

    |

  3. Differentiate (sin^(-1)x^4)^4 with respect to x :

    Text Solution

    |

  4. Differentiate sin^(-1)(x/(sqrt(x^2+a^2))) with respect to x :

    Text Solution

    |

  5. Differentiate (e^xsinx)/((x^2+2)^3) with respect to x .

    Text Solution

    |

  6. Differentiate 3\ e^(-3x)log(1+x)

    Text Solution

    |

  7. Differentiate the following functions with respect to (x^2+2)/(sqrt...

    Text Solution

    |

  8. Differentiate (x^2(1-x^2)^3)/(cos2x) with respect to x .

    Text Solution

    |

  9. Differentiate log{cot(pi/4+x/2)} with respect to x :

    Text Solution

    |

  10. Differentiate the following functions with respect to e^(a x)secxta...

    Text Solution

    |

  11. Differentiate log(cosx^2) with respect to x :

    Text Solution

    |

  12. Differentiate cos(logx)^2 with respect to x :

    Text Solution

    |

  13. Differentiate logsqrt((x-1)/(x+1)) with respect to x :

    Text Solution

    |

  14. If y=log{sqrt(x-1)-sqrt(x+1)} , show that (dy)/(dx)=(-1)/(2sqrt(x^2-1)...

    Text Solution

    |

  15. If y=sqrt(x+1)+sqrt(x-1) , prove that sqrt(x^2-1)(dy)/(dx)=1/2y

    Text Solution

    |

  16. If y=x/(x+2) , prove that x(dy)/(dx)=(1-y)y

    Text Solution

    |

  17. If y=log(sqrt(x)+1/(sqrt(x))) , prove that (dy)/(dx)=(x-1)/(2x(x+1))

    Text Solution

    |

  18. If y=logsqrt((1-tanx)/(1+tanx)) , prove that (dy)/(dx)=-sec2x .

    Text Solution

    |

  19. If y=sqrt(x)+1/(sqrt(x)) , prove that 2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

    Text Solution

    |

  20. If y=(xsin^(-1)x)/(sqrt(1-x^2)) , prove that (1-x^2)(dy)/(dx)=x+y/x .

    Text Solution

    |