• Sourcing Solutions
  • Services & Membership
  • Help & Community
About product and suppliers:
        Q: Is x-1 the same as lnx?
A: The product rule sates : d / dx ultraviolet = v du / dx + u dv / dx It 're not very clear-cut what your denominator is : . `` over one + ( x squared ) '' : d / dx ( x / 1+x 2 ) d / dx ( x / 1+x 2 ) = d / dx x ( 1 + x 2 ) -1 . = ( 1 + x 2 ) -1 d / dx x + x d / dx ( 1 + x 2 ) -1 = ( 1 + x 2 ) -1 + x -2x ( 1 + x 2 ) -2 = ( 1 + x 2 ) -2 ( 1 + x 2 - 2x 2 ) = ( 1 - x 2 ) / ( 1 + x 2 ) 2 . `` over ( 1 + x ) [ all ] squared '' : d / dx ( x / ( 1+x ) 2 ) d / dx ( x / ( 1+x ) 2 ) = d / dx x ( 1 + x ) -2 . = ( 1 + x ) -2 d / dx x + x d / dx ( 1 + x ) -2 = ( 1 + x ) -2 + x -2 ( 1 + x ) -3 = ( 1 + x ) -3 ( 1 + x - 2x ) = ( 1 - x ) / ( 1 + x ) 3 . If you 'd prefer , you are able use the quotient rule : d / dx ( u / v ) = ( v du / dx - u dv / dx ) / v 2 .