How do you differentiate #f(x) = (x-1)(x-2)# using the product rule?

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Answer 1 · 2016-06-08T23:38:48

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

In our case, let #f(x) = g(x) xx h(x)#

Therefore, #g(x) = x - 1# and #h(x) = x - 2#

Let's differentiate both these functions.

#g'(x) = 1#

and

#h'(x) = 1#

Now, we can apply the product rule.

#f'(x) = (g'(x) xx h(x)) + (h'(x) xx g(x))#

#f'(x) = ((x - 2) xx 1) + ((x - 1) xx 1)#

#f'(x) = x - 2 + x - 1#

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

Therefore #dy/dx = 2x - 3#

Hopefully this helps!