How do you differentiate #g(y) =(60x^2+74)( 2x+2) # using the product rule?

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Answer 1 · 2017-07-14T00:54:46

#g'(x) = color(blue)(360x^2 + 240x + 148#

NOTE: I might add that the function should be of #g(x)#, not #g(y)# (there is no #y#-variable).

We're asked to find the derivative

#(dg)/(dx) [(60x^2+74)(2x+2)]#

The product rule is

#d/(dx) [uv] = v(du)/(dx) + u(dv)/(dx)#

where

#= (60x^2+74)(d/(dx)[2x+2]) + (2x+2)(d/(dx)[60x^2+74])#

Applying the power rule to both terms, we have

#= (60x^2+74)(2) + (2x+2)(120x)#

#= 120x^2 + 148 + 240x^2 + 240x#

#= color(blue)(360x^2 + 240x + 148#