Are Trig Identities Needed for This Derivative Problem?

[asdfsystema]

Homework Statement

Homework Equations

Trig identities or straightforward derivative?

The Attempt at a Solution

Is the answers

1. C
2. B
3. A
4. D

I tried taking the derivative of these, but a friend of mine here told me it deals with trig identities and isn't a derivative equation at all. Is he wrong ?

I am pretty sure these are the solutions but i want to double check ...

 

[Mark44]

Your friend is wrong. You hae to take the derivatives of the four given functions, and then match the derivatives you got with the answers shown by using trig identities. For 1, C is correct. For the rest, use trig identities to simplify the answers and compare your results with the derivatives you got for the given functions.

 

[asdfsystema]

2. y= tan(x)
y'= sec^2(x)
Answer: D
trig identity used: 1+tan^2(x)= sec^2(x)

3. y=cos(tan(x))
y'= -sec^2(x)*sin(tan(x))
Answer: A

4.y=sin(x)tan(x)
y'=cos(x)*tan(x)+sec^2(x)*sin(x)
Answer: B

Is this correct? Thank you for the quick response by the way.

 

[Mark44]

Yep, yep, and yep.

 

[asdfsystema]

Thank you ! problem solved