How do you differentiate #y=(1+sinx)/(x+cosx)#?

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Answer 1 · 2016-10-18T19:16:38

#f'(x) = {(x)cos(x)}/(x + cos(x))^2#

Given: #f(x) = g(x)/(h(x))#

#f'(x) = {g'(x)h(x) - g(x)h'(x)}/(h(x))^2#

#g(x) = 1 + sin(x)#
#g'(x) = cos(x)#
#h(x) = x + cos(x)#
#h'(x) = 1 - sin(x)#

#f'(x) = {(cos(x))(x + cos(x)) - (1 + sin(x))(1 - sin(x))}/(x + cos(x))^2#

#f'(x) = {(x)cos(x) + cos^2(x) - (1 - sin^2(x))}/(x + cos(x))^2#

#f'(x) = {(x)cos(x) + cos^2(x) - (cos^2(x))}/(x + cos(x))^2#

#f'(x) = {(x)cos(x)}/(x + cos(x))^2#