Differentiate $s=(1+sint)/(1+tant)$ using the quotient rule?

Question

The answer is

$(cost(1+tant)-sec^2t(1+sint))/(1+tant)^2$

1218 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-05T05:12:58

Please see below.

According to Quotient rule, if $s(t)=(g(t))/(h(t))$

then $(ds)/(dt)=((dg)/(dt)xxh(t)-(dh)/(dt)xxg(t))/(h(t))^2$

Here in $s(t)=(1+sint)/(1+tant)$ ,

$g(t)=1+sint$ and $(dg)/(dt)=cost$ and

$h(t)=1+tant$ and $(dh)/(dt)=sec^2t$

Hence $(ds)/(dt)=(cost(1+tant)-sec^2t(1+sint))/(1+tant)^2$