onesun0000
Junior Member
- Joined
- Dec 18, 2018
- Messages
- 83
First of all, maybe this will help, I know how to derive the derivative of sec(x) using quotient rule. In the steps, I understand step 1 because thats like multiplying by reciprocal that's why it's equal to 1. In step two, since [MATH]\sec(x) \cos(x)=1[/MATH], its derivative is zero because the drivative of a constant is zero. In step 3, that's where the product rule is used, which is used correctly. In step 4, I quite understand it, in a sense that I think quotient rule is used there. That's why I don't understand if there is an error or not. It seems no error at all. But my gut says there is. I am not sure.It's quite difficult to respond to this post. Our aim is to increase YOUR understanding, that's why we ask you to show YOUR work so that we can see where you are stuck. However you have shown a friend's work and stated that you don't understand either the original question or your friend's answer.
So, to start off, please tell us which "step" (step 1, step 2, etc) of the original question you don't understand and try to tell us why you don't understand it so that we can help YOU out.
My friend also said this.I second Cubist’s reply, but have some additional comments.
You seem to believe that the derivation is in error. Why do you think so? What do you think the derivative of sec(x) is?
What is the course in which this problem is posed?
It is of course true that the secant is not everywhere defined and that therefore its derivative is not everywhere defined. But that is true whether you use the quotient rule, the power rule, or the product rule. So your friend’s answer is completely irrelevant.
Yes, Bob's method has an error in it! One can argue that Bob got the correct answer but he surely used a wrong method.My friend also said this.
View attachment 22548
Step3) [MATH]\dfrac{d}{dx}sec(x)*cos(x)-sec(x)*sin(x) = 0[/MATH] so [MATH]\dfrac{d}{dx}sec(x)*cos(x)=sec(x)*sin(x)[/MATH] then [MATH]\dfrac{d}{dx}sec(x) \dfrac{sec(x)*sin(x)}{cos(x)} = sec(x)*tan(x)[/MATH].In step 4, I quite understand it, in a sense that I think quotient rule is used there.
That's how I use quotient rule to derive the derivative of [MATH]\sec(x)[/MATH]. So is there an error on the steps?The proof by your friend is fine. I felt it was an unusual way of doing it but that's my problem.
I (all of us I am sure) would like to see your proof that you speak of using the quotient rule. Can you please post it.
Personally I would never use the quotient rule if the numerator or denominator is a constant. sec(x) = 1/cos(x) = (cos(x))-1. I would use the power rule from here to compute the derivative of sec(x). Give it a try and post back with your work.
Perfect!!That's how I use quotient rule to derive the derivative of [MATH]\sec(x)[/MATH]. So is there an error on the steps?
View attachment 22551
so on my original question, is there an error? or none?Perfect!!
As I said in my earlier post your friends proof was fine.so on my original question, is there an error? or none?
so the error is on step 3?As I said in my earlier post your friends proof was fine.
A fine proof has no errors!oh
so the error is on step 3?
JomoA fine proof has no errors!
In an earlier post you said that you did not understand how to go from step 3 to step 4 so I filled in some of the missing steps. There were no errors in the original proof which you posted.