If y = (sin x)x + sin-1 (x)1/2, find dy/dx

Mention each and every step

Asked by haroonrashidgkp | 19th Jun, 2018, 10:54: PM

Expert Answer:

y = (sin x)x + sin-1 (x)1/2 
y = u + v
u = (sin x)x 
log u = xlogsinx
begin mathsize 16px style 1 over straight u cross times du over dx equals straight x cross times fraction numerator 1 over denominator sin begin display style straight x end style end fraction cross times cosx plus logsinx
fraction numerator begin display style du end style over denominator begin display style dx end style end fraction equals open parentheses sinx close parentheses to the power of straight x space open parentheses xcotx plus logsinx close parentheses end style
v = sin-1 (x)1/2 
begin mathsize 16px style dv over dx equals fraction numerator 1 over denominator square root of 1 minus straight x end root end fraction cross times fraction numerator 1 over denominator 2 square root of straight x end fraction end style
begin mathsize 16px style dy over dx equals open parentheses sinx close parentheses to the power of straight x space open parentheses xcotx plus logsinx close parentheses plus fraction numerator 1 over denominator 2 square root of straight x open parentheses 1 minus straight x close parentheses end root end fraction end style

Answered by Sneha shidid | 20th Jun, 2018, 09:35: AM