How do you differentiate #g(x) = (x+4)(x^2-2)# using the product rule?

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Answer 1 · 2016-03-01T01:05:39

#g'(x)=3x^2+8x-2#

The product rule states that

#d/dx(f(x)h(x))=h(x)f'(x)+f(x)h'(x)#

Here, the two functions being multiplied by one another are:

#f(x)=x+4#
#h(x)=x^2-2#

We can find each of their derivatives through the power rule.

#f'(x)=1#
#h'(x)=2x#

Plugging these into the original expression, we see that

#g'(x)=(x^2-2)(1)+(x+4)(2x)#

#g'(x)=x^2-2+2x^2+8x#

#g'(x)=3x^2+8x-2#