if y=log sin x/cos log x,then find dy/dx

Asked by aashu.60 | 25th Nov, 2015, 06:04: AM

Expert Answer:

begin mathsize 11px style y equals fraction numerator log sin x over denominator cos log x end fraction rightwards double arrow y open parentheses cos log x close parentheses equals log sin x rightwards double arrow fraction numerator d y over denominator d x end fraction open parentheses c o s l o g x close parentheses plus y open parentheses negative sin log x open parentheses 1 over x close parentheses close parentheses equals fraction numerator 1 over denominator sin x end fraction cos x rightwards double arrow fraction numerator d y over denominator d x end fraction open parentheses c o s l o g x close parentheses equals fraction numerator l o g s i n x over denominator c o s l o g x end fraction open parentheses s i n l o g x open parentheses 1 over x close parentheses close parentheses plus c o t x rightwards double arrow fraction numerator d y over denominator d x end fraction open parentheses c o s l o g x close parentheses equals fraction numerator log sin x open parentheses tan log x close parentheses over denominator x end fraction plus c o t x rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator l o g s i n x open parentheses t a n l o g x close parentheses over denominator x open parentheses c o s l o g x close parentheses end fraction plus fraction numerator c o t x over denominator open parentheses c o s l o g x close parentheses end fraction end style

Answered by satyajit samal | 25th Nov, 2015, 11:53: AM