How do you differentiate #f(x)=xsecx# using the product rule?

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Answer 1 · 2016-03-27T05:14:22

#f' (x)=sec x+x*sec x tan x#

We start from the given equation
#f(x)=x sec x#

We will use the derivative of product formula

#d/dx(uv)=v*d/dx(u)+u*d/dx(v)#

Let #u=x# and #v=sec x#

#d/dx(f(x))=d/dx(x sec x)=sec x*d/dx(x)+x*d/dx(sec x)#

#d/dx(f(x))=(sec x)(1)+x(sec x tan x)d/dx(x)#

#d/dx(f(x))=sec x+x(sec x tan x)*1#

#d/dx(f(x))=sec x+x*sec x tan x#

God bless....I hope the explanation is useful