Question

PLEASE HELP! MEDAL WILL BE REWARDED!
FIND THE DERIVATIVE:
f(x)=secx-sqrt2 tanx
Is the answer sec^2(x)[sin(x) - √2] or
f(x) = sec(x) - (sqrt(2) * tanx)???

Answer 1

@jim_thompson5910

Answer 2

what's the derivative of sec(x)?

Answer 3

its secx tanx

Answer 4

what is the derivative of tan(x)?

Answer 5

sec^2x

Answer 6

and just so I have it correct, the original function is

\[\large f(x) = \sec(x) - \sqrt{2}*\tan(x)\]

right? and the tan(x) is NOT in the square root right?

Answer 7

yes you are correct

Answer 8

so that would mean that we would get this

\[\large f(x) = \sec(x) - \sqrt{2}*\tan(x)\]

\[\large \frac{d}{dx}[f(x)] = \frac{d}{dx}[\sec(x) - \sqrt{2}*\tan(x)]\]

\[\large \frac{d}{dx}[f(x)] = \frac{d}{dx}[\sec(x)] - \frac{d}{dx}[\sqrt{2}*\tan(x)]\]

\[\large f^{\prime}(x) = \sec(x)\tan(x) - \sqrt{2}*\sec^2(x)\]

\[\large f^{\prime}(x) = \sec(x)\left[\tan(x) - \sqrt{2}*\sec(x)\right]\]

Note: the last step is entirely optional really (since it's just factoring out the GCF)

Answer 9

Thank you so much!!!!

Answer 10

sure thing