How do you find the derivative of # ( cos (x) ) / ( 2 + sin (x) )#? Calculus Differentiating Trigonometric Functions Derivative Rules for y=cos(x) and y=tan(x) 1 Answer Dharma R. Sep 26, 2015 #(-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# Answer link Related questions What is the derivative of #y=cos(x)# ? What is the derivative of #y=tan(x)# ? How do you find the 108th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x)# from first principle? How do you find the derivative of #y=cos(x^2)# ? How do you find the derivative of #y=e^x cos(x)# ? How do you find the derivative of #y=x^cos(x)#? How do you find the second derivative of #y=cos(x^2)# ? How do you find the 50th derivative of #y=cos(x)# ? How do you find the derivative of #y=cos(x^2)# ? See all questions in Derivative Rules for y=cos(x) and y=tan(x) Impact of this question 2134 views around the world You can reuse this answer Creative Commons License