Question

Calculus Help! (Derivatives)

Find the derivative of f(x)=arc sec(2x)

Answer 1

I thinks that's the answer 2/2x\[sqrt{4x^2-1}\]

Answer 2

-2/2xsqrt4x^2-1

Answer 3

@imer: would you please provide some framework for Mike_Petro so that he himself can answer this question. for example, you could type in\[\frac{ d }{ dx }\sin ^{-1}u=\frac{ \frac{ du }{ dx } }{ \sqrt{1-u^2} }\] and mention that u is itself a function of x.

Answer 4

explanation coming in a bit.

Answer 5

Yeah, the answer is great, but I'd like to be able to answer trig^-1 functions when test time comes! :) Thanks everyone in advanced

Answer 6

@imer: Thank you. Mind reversing the order? Explanation first. Formula second. Guide the student towards solving his/her own question, third.

Answer 7

@Mike_Petro: Glad to have your input. Tell the rest of us what you would like to know, or practice. We'll gladly help you solve your own math problems.

Answer 8

I usually go around giving the answer and then explain the concept . Some times the person knows the answer but wants to verify.

Answer 9

I'm doing a review for my exam a bit later, but a few problems are tripping me up like Integrals or exponential functions and trigonometric problems

Answer 10

@imer So I got the answer, is there a property or a set formula for these Trig^-1 functions?

Answer 11

Happy to help. Please post specific problems. Share your throughts about them. Separate what you know from what you don't. One of us will be delighted to respond.

Answer 12

I would recommend you to call them arc-trig functions and yes they are quite similar if you know the derivative of regular trig functions.

Answer 13

I will be explaining in a bit how they are derived.

Answer 14

Okay because I'm on another arc-trig function but it says not to use a calculator its
sec(arctan(-3/5))
but since I cant use a calculator I'm assuming there is a set property sort of like cos x = sin x + c

Answer 15

lets start with simple one.
\[y= \arcsin(x)\]
If you are aware of implicit differentiation, then you can go around with this problem. \[y= \arcsin(x) \rightarrow \sin(y)=x\]

Do you catch it?

Answer 16

So, arctan(x)=tan(y)?

Answer 17

Mike: This problem has nothing to do with integration, so your "cos x = sin x + c" is out of place here. Your topic here is "inverse trig functions."

It's very important that you recognize that "artcan(-3/5)" is an ANGLE. It's possible, but totally unnecessary, to find that angle using a calculator. So scratch that. Instead, draw a picture of a triangle whose tangent is (-3/5):

Answer 18

NO, \[\arctan(y)=x\]
\[y=\arctan()\]
It same as saying if arctan(x) gives me angle "y", then tan(y) will be give me "x"

Answer 19

@mathmale So I drew the triangle and the hypotenuse is sqrt(34) or 5.8, but how do I use it to find the answer?
@imer OK so, if arctan(x)=y then tan(y)=x?

Answer 20

Its same as saying \[y=x^1/2\] is \[y^2=x\]