How do you differentiate #g(x) =x (4x^6 + 5) # using the product rule?

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Answer 1 · 2016-04-24T13:58:03

#28x^6+5#

The product rule says that if

#g(x)=a(x)*b(x)#

then

#g'(x)=a'(x)b(x)+a(x)b'(x)#

Substituting in from the question, #a(x)=x# and #b(x)=4x^6+5#, then

#a'(x)=1#

#b'(x)=24x^5#

Now we can find that

#g'(x)=1(4x^6+5)+x(24x^6)#

and, on expanding the brackets,

#=28x^6+5#

You can check this answer by distributing the function and just using the power rule:

#g(x)=4x^7+5x#

#g'(x)=28x^6+5#