How do you differentiate #g(y) =(4x^2+5)(x^2 - 1) # using the product rule?

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Answer 1 · 2016-06-19T00:34:12

The product rule states that for a function #f(x) = g(x)h(x)#, #f'(x)# is given by #g'(x) xx h(x) + g(x) xx h'(x)#.

Let #4x^2 + 5# be #g(x)# and #x^2 -1 # be #h(x)# and your whole function be #f(x)# (instead of #g(y))#.

#g'(x) = 8x#

#h'(x) = 2x#

Thus, we have that #f'(x) = (8x(x^2 - 1)) + (2x(4x^2 + 5))#

#f'(x) = 8x^3 - 8x + 8x^3 + 10x#

#f'(x) = 16x^3 + 2x#

Hopefully this helps!