Asked by Topperlearning User | 25th Jul, 2014, 04:40: PM

Expert Answer:

H e r e space f left parenthesis x right parenthesis equals fraction numerator x over denominator sin to the power of n x end fraction
f apostrophe left parenthesis x right parenthesis equals fraction numerator d over denominator d x end fraction open square brackets fraction numerator x over denominator sin to the power of n x end fraction close square brackets
equals fraction numerator sin to the power of n x begin display style fraction numerator d over denominator d x end fraction end style left parenthesis x right parenthesis minus x begin display style fraction numerator d over denominator d x end fraction end style left parenthesis sin to the power of n x right parenthesis over denominator open parentheses sin to the power of n x close parentheses squared end fraction
equals fraction numerator begin display style sin to the power of n x.1 minus x. n sin to the power of n minus 1 end exponent x. cos space x end style over denominator open parentheses sin to the power of n x close parentheses squared end fraction
equals fraction numerator begin display style sin to the power of n minus 1 end exponent x. open parentheses sin space x minus n space cos space x close parentheses end style over denominator sin to the power of 2 n end exponent x end fraction
equals fraction numerator begin display style open parentheses sin space x minus n space cos space x close parentheses end style over denominator sin to the power of 2 n minus n plus 1 end exponent x end fraction
equals fraction numerator begin display style open parentheses sin space x minus n space cos space x close parentheses end style over denominator sin to the power of n plus 1 end exponent x end fraction

Answered by  | 25th Jul, 2014, 06:40: PM