How do you differentiate #f(x)=(x^3-4)(x^2-3)# using the product rule?

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Answer 1 · 2018-04-23T19:47:12

#3x^2(x^2-3) + "2x(x^3-4)#

when two distinct functions are multiplied together:

#f(xy) = (x^3-4)(x^2-3)#

We can use the product rule to work out the differential:

# f'(xy) = f(x) * f'(y) + f(y) * f'(x) #

# f(x) = (x^3−4)#
# f'(x) = 3x^2 #

#f(y) = (x^2-3)#
#f'(y) = 2x#

Can also be written as #(uv)' = uv' + vu' #
# u = (x^3−4)#
# u' = 3x^2 #
#v = (x^2-3)#
#v' = 2x#