If #f(x)= sec 4 x # and #g(x) = 2 x #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
bp
Apr 30, 2016

8 sec8x tan 8x

Explanation:

f(g(x)=sec4(2x) =sec 8x

Chain rule in simple words is that if z is a function of t and t is a function of x, the #dz/dx= dz/dt .dt/dx#. Inthis case

let g(x) = t= 2x, so f(g(x)= f(t)= sec4t
Hence #(d(sec4t))/dx= (df)/dt. dt/dx=(d(sec4t))/dt (d(2x))/dx#

#=4sec 4t tan4t (d(2x))/dx #

= 4 sec 4t tan 4t (2)

=8 sec8x tan 8x

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