1. ## Derivative confusion

I'm confused....is $\displaystyle sec x^2$ the same thing as $\displaystyle sec^2 x$? I was told you rewrite these as $\displaystyle sec (x^2) and (sec x)^2$, respectively.

Now I have a problem and I'm unsure how to do it since I don't know the above rule:

Find the derivative of f(Θ) = secΘ^2

How would you rewrite this and how would you proceed?
If I treat it as (secΘ)^2 I get: 2secΘ^2(tanΘ)

Thanks=]

2. Originally Posted by janedoe
I'm confused....is $\displaystyle sec x^2$ the same thing as $\displaystyle sec^2 x$? I was told you rewrite these as $\displaystyle sec (x^2) and (sec x)^2$, respectively.

Now I have a problem and I'm unsure how to do it since I don't know the above rule:

Find the derivative of f(Θ) = secΘ^2

How would you rewrite this and how would you proceed?
If I treat it as (secΘ)^2 I get: 2secΘ^2(tanΘ)

Thanks=]
What you've posted has several interpretations. Ask your instructor which one is intended.

3. Originally Posted by janedoe
I'm confused....is $\displaystyle sec x^2$ the same thing as $\displaystyle sec^2 x$? I was told you rewrite these as $\displaystyle sec (x^2) and (sec x)^2$, respectively.

Now I have a problem and I'm unsure how to do it since I don't know the above rule:

Find the derivative of f(Θ) = secΘ^2

How would you rewrite this and how would you proceed?
If I treat it as (secΘ)^2 I get: 2secΘ^2(tanΘ)

Thanks=]
According to math notations, $\displaystyle sec x^2=sec(x^2)$ (squared first, sec second) and $\displaystyle sec^2 x=(secx)^2$ (sec first, squared second).