If #f(x)= cos(-2 x -1) # and #g(x) = 4x^2 -5 #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2016-03-18T10:33:01

#(df)/(dx)=-16xsin(8x^2-9)#

Note that #cos(-2x-1)=cos(2x+1)# as #cos(-theta)=costheta#.

If #f(x)=cos(-2x-1)# and #g(x)=4x^2-5#

#f(g(x))=cos(2(4x^2-5)+1)#

As according to chain rule, #(df)/(dx)=(df)/(dg)xx(dg)/(dx)#

#(df)/(dx)=-2sin(2(4x^2-5)+1)xxd/(dx)(4x^2-5)#

= #-2sin(2(4x^2-5)+1)xx8x)#

= #-16xsin(8x^2-9)#