Using quotient rule, we have `(dy)/(dx)=(d)/(dx)((e^(x))/(1+ sin x))` `=((1+ sin x)cdot(d)/(dx)(e^(x))-e^(x)cdot(d)/(dx)(1+ sin x))/(1+ sin x )^(2)` `=((1+sin x)cdote^(x)-e^(x)cdot(0 + cos x))/((1+ sin x)^(2))=(e^(x)(1+ sin x - cos x))/((1+ sin x )^(2))`
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