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

2 Answers
Mar 7, 2016

#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#

Mar 7, 2016

#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#