Question

Derive secx-Sqrt(2)tanx

I get sinx/(sqrt(2)cos)^2

But it says the answer is sec(x)tan(x)-sqrt(2)sec^2(x)

how do I do it?

Answer 1

alright, lets look at the formula

\[\sec x-\sqrt{2}\tan x\]

Answer 2

moving from the left to the right, the derivative of sec x is Sec x Tan x

Answer 3

then going to the right, to find the derivative of \[\sqrt{2}\tan x\] we need to use the chain rule

Answer 4

er my bad, not chain rule, product rule

Answer 5

say \[\sqrt{2}=u\]

and tan x = v

Answer 6

product rule is uv' + vu'

Answer 7

now plug it in, derivative of tan x is sec^2 x and the derivative of sqrt(2) is 0
so the derivative of sqrt(2) tan x is
\[\sqrt{2}\sec ^{2}x\]

Answer 8

now to put it together,
\[\sec x \tan x-\sqrt{2}\sec ^{2}x\]

Answer 9

differentiate not derive!