differentiate:
y= 1+sin x / (x+ cos x)
I dont know how to do this one...can someone help me out?
given the quotient rule which states $\displaystyle \frac{d}{dx}f(x)$ when $\displaystyle f(x)=\frac{g(x)}{h(x)}$ is equal to $\displaystyle \frac{g'(x)h(x)-g(x)h'(x)}{(h(x))^2}$
therefore:
$\displaystyle g(x)=1+\sin(x), h(x)=x+\cos(x)$
so
$\displaystyle y'=\frac{(0+\cos(x)*1)(x+\cos(x))-[(1+\sin(x))(1*x^0-\sin(x)*1)]}{(x+\cos(x))^2}
$
You can leave it like that or expand it out.