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

1 Answer
Dharma R.
Sep 26, 2015

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

Explanation:

f(x)=cosx/(2+sinx)f(x)=cosx2+sinx
let u(x)=cos(x)u(x)=cos(x) and v(x)=2+sinxv(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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