Question

what is the second derivative of sec(x+2)

Answer 1

Do you remember the first derivative of sec(x)? :-)

Answer 2

no

Answer 3

The derivative of sec(x) = sec(x) tan(x). Now, you have to apply the product rule: derivative of tan(x) = sec^2(x).

Answer 4

Sec(x+2) x tan(x+2) is the first derivative

Answer 5

Use product rule

Answer 6

Because the inside derivative is 1, you don't need to apply the chain rule :-)

Answer 7

ok is it the product of chain , You giving two different answers

Answer 8

No, I am talking about sec(x). As you wish to work with x+2, just substitute it. Nothing will be changed, because the inside derivative with respect to x is 1. If you prefer, do the product rule on sec(x+2) tan(x+2).

Answer 9

ok i will be back with solution to check and see if im on track

Answer 10

OK then :-)

Answer 11

I GOT PI^2(SIN(X+2)^2+1/COS(X+2)^3

Answer 12

Pi? How did you get to that: \[ \frac{d(\sec(x+2)\tan(x+2))}{dx} = \sec(x+2) \frac{d(\tan(x+2))}{dx} + \tan(x+2) \frac{d(\sec(x+2))}{dx}\]

Answer 13

\( d(\tan(x+2))/dx = \sec^2x \) and \( d(\sec(x+2))/dx = \sec(x+2)\tan(x+2)\)

Answer 14

idk , the second deriv are a problem the first arent bad

Answer 15

I mean, sec^2(x+2) for the first sec up there.

Answer 16

The second derivative is the same thing as taking the first derivative. Shouldn't be any harder :_)

Answer 17

well calculus period is pointless lol but i till have to take it

Answer 18

Calculus is one of the culminations of thousands of years of human effort, I would hardly call it pointless. If you need an application, read up on how calculus is used in physics. Hint: it's everywhere.

Answer 19

well I know it help humans and its history but In real life , not needed

Answer 20

In real life it's used on a daily basis by professionals in countless fields, all of whom are paid well because they took the time to learn calculus when they were in school.

Answer 21

Furthermore, learning calculus helps you train your mind to think logically and rigorously, which is a skill that is very hard to gain and is literally priceless.

Answer 22

The same argument can be applied to playing violin, studying history or economics, doing a sport. By your logic, should we only be concerned about survival? The very fact that we went beyond "real" life is a monument to the human intellect and reasoning, as the violin :-). Abstractions are the corner stone of our age and of what we've achieved, for higher thoughts need a higher language :-)