Trig Derivative with Sec and Tan

[Jason76]

\(\displaystyle y = \sec(x)\tan(x)\)

\(\displaystyle y' = [\tan(x)][\dfrac{d}{dx}(sec(x))] + [\sec(x)][\dfrac{d}{dx}(\tan(x))]\)

\(\displaystyle y' = [\tan(x)][\sec(x)\tan(x)] + [\sec(x)][\sec^{2}(x)]\)

 

[Deleted member 4993]

\(\displaystyle y = \sec(x)\tan(x)\)

\(\displaystyle y' = [\tan(x)][\dfrac{d}{dx}(sec(x))] + [\sec(x)][\dfrac{d}{dx}(\tan(x))]\)

\(\displaystyle y' = [\tan(x)][\sec(x)\tan(x)] + [\sec(x)][\sec^{2}(x)]\)

What is the confusion?!

 

[Jason76]

What is the confusion?!

So that's the answer?

 

[Jason76]

The computer said the answer is right.

 

[lookagain]

\(\displaystyle y = \sec(x)\tan(x)\)

\(\displaystyle y' = [\tan(x)][\dfrac{d}{dx}(sec(x))] + [\sec(x)][\dfrac{d}{dx}(\tan(x))]\)

\(\displaystyle y' = [\tan(x)][\sec(x)\tan(x)] + [\sec(x)][\sec^{2}(x)] \ \ \ \ <---- \)

The computer said the answer is right.

I don't know why the computer would accept that answer form above as right, because it has not been taken far enough.

It should accept it, for instance, when it can it is presented as \(\displaystyle \ y' \ = \ [\sec(x)][\tan^2(x)] \ + \ [\sec^3(x)] \ \ \) (but not only in this form).