How do you differentiate $f(x) =cosx*sec^2(x)$ ?

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How do you differentiate $f(x) =cosx*sec^2(x)$ ?

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Answer 1 · 2016-03-07T13:27:07

$d/(d x) f(x)=sec^2 x$

Explanation:

$d/(d x) f(x)=-sin x *sec^2 x+ 2secx*sec x*tan x*cos x$
$d/(d x) f(x)=-sin x *sec^2 x+ 2sec^2x*tan x*cos x$
$d/(d x) f(x)=sec^2(-sin x+tan x*cos x)" , "tan x=(sin x)/(cos x)$
$d/(d x) f(x)=sec^2 x(-sin x+(sin x)/cancel(cos x)*cancel(cos x))$
$d/(d x) f(x)=sec^2 x(cancel(-sin x)+cancel(sin x))$
$d/(d x) f(x)=sec^2 x$

Answer 2 · 2016-03-07T14:35:31

$f'(x) = secxtanx$ . Here are two ways to get this answer.

Explanation:

Rewrite first

$f(x)=cosxsec^2x$

$= cosx 1/(cosx)^2$

$= 1/cosx$

$= secx$ .

So,

$f'(x) = secxtanx$ .

Use product rule first
$f(x)=cosxsec^2x$

$f'(x) = (-sinx)(sec^2x)+(cosx)(2secx*secxtanx)$

$= -sinxsec^2x+2sec^2x [tanx cosx]$

$= -sinxsec^2x+2sec^2x [sinx]$

$= sec^2xsinx$

$= secx tanx$

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How do you differentiate $f(x) =cosx*sec^2(x)$ ?

2 Answers

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How do you differentiate f(x) =cosx*sec^2(x) f(x) =cosx*sec^2(x) ?

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How do you differentiate $f(x) =cosx*sec^2(x)$ ?