Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Quotient Rule

Given y = (sec t)/(1 + t sin t), find y prime.

I will not show all my work via cell phone. It takes to long to type all the math work.

Here is where I am:
 
y' = [(sec t•tan t)(1 + t sint) - sec t•sin t + t sec t cost t]/(1 + t sint)^2

Stuck here....

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Quotient Rule

You might like to use the fact that:

sec(t)*cos(t) = 1

and

sec(t)*sin(t) = tan(t)

Can you see why these are true?

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Quotient Rule

You might like to use the fact that:

sec(t)*cos(t) = 1

and

sec(t)*sin(t) = tan(t)

Can you see why these are true?

Let me see. I think using trigonometric identities helps out here.

sec (t) = 1/cos(t).

sec(t)cos(t) becomes 1/cos(t) • cos(t) = cos(t)/cos(t) = 1.

So, sec (t) sin(t) becomes 1/cos(t) sin(t) = sin(t)/cos(t) = tan(t).

The problem now becomes all too clear.

Thanks.