1. dy/dx of log 10 to the base x
  2. dy/dx of log x to the base 10

Asked by parthpatel.pp802 | 30th Apr, 2014, 02:50: AM

Expert Answer:

1. space G i v e n space t h a t space y equals log subscript x 10 W e space k n o w space t h a t comma space open parentheses space ln subscript e x close parentheses cross times open parentheses ln subscript x 10 close parentheses equals ln subscript e 10 rightwards double arrow ln subscript x 10 equals fraction numerator space ln subscript e 10 over denominator ln subscript e x end fraction rightwards double arrow space y equals fraction numerator space ln subscript e 10 over denominator ln subscript e x end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator minus ln open parentheses 10 close parentheses over denominator x cross times open parentheses ln open parentheses x close parentheses close parentheses squared end fraction
2. space G i v e n space t h a t space y equals log subscript 10 x W e space k n o w space t h a t comma space ln subscript e 10 cross times ln subscript 10 x equals ln subscript e x rightwards double arrow ln subscript 10 x equals fraction numerator ln subscript e x over denominator ln subscript e 10 end fraction rightwards double arrow y equals fraction numerator ln subscript e x over denominator ln subscript e 10 end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator x cross times ln subscript e 10 end fraction

Answered by  | 30th Apr, 2014, 09:21: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.