How do you find the derivative of # ( cos (x) ) / ( 2 + sin (x) )#?

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How do you find the derivative of # ( cos (x) ) / ( 2 + sin (x) )#?

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Answer 1 · 2015-09-26T13:25:05

#(-2sinx-1)/(2+sinx)^2#

Explanation:

#f(x)=cosx/(2+sinx)#
let #u(x)=cos(x)# and #v(x)=2+sinx#
then #u'(x)=-sinx# and #v'(x)=cosx#
#f(x)=(u(x))/(v(x))#
#f'(x)=1/(v(x)^2)[v(x)u'(x)-u(x)v'(x)]#
#f'(x)=1/(2+sinx)^2[(2+sinx)(-sinx)-cosx(cosx)]=(-2sinx-1)/(2+sinx)^2#

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How do you find the derivative of # ( cos (x) ) / ( 2 + sin (x) )#?

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