x/sinnx

find derivative

Asked by Dharvi Kumra | 3rd Dec, 2014, 10:26: PM

Expert Answer:

G i v e n space t h a t space y equals fraction numerator x over denominator sin to the power of n x end fraction rightwards double arrow y equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction comma space w h e r e space f open parentheses x close parentheses equals x space a n d space g open parentheses x close parentheses equals sin to the power of n x T h e r e f o r e space w e space n e e d space t o space a p p l y space q u o t i e n t space r u l e. T h u s comma fraction numerator d y over denominator d x end fraction equals fraction numerator g open parentheses x close parentheses cross times f apostrophe open parentheses x close parentheses minus f open parentheses x close parentheses cross times g apostrophe open parentheses x close parentheses over denominator open square brackets g open parentheses x close parentheses close square brackets squared end fraction D i f f e r e n t i a t i n g space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma fraction numerator d y over denominator d x end fraction equals fraction numerator sin to the power of n x cross times 1 minus x cross times n cross times sin to the power of n minus 1 end exponent open parentheses x close parentheses over denominator open square brackets sin to the power of n x close square brackets squared end fraction equals fraction numerator sin to the power of n x minus x n cross times sin to the power of n minus 1 end exponent open parentheses x close parentheses over denominator open square brackets sin to the power of n x close square brackets squared end fraction

Answered by Vimala Ramamurthy | 4th Dec, 2014, 08:50: AM