Could someone please help me solve this
If f(2)=f'(2)=g'(2)=g(2)=2, find (fg)'(2).
How would I solve this, I am completely lost as to what I would do.
To find the derivative of the product of two functions, (fg)'(x), you can use the product rule, which states that (fg)'(x) = f'(x)g(x) + f(x)g'(x).
In this case, we're given the values of f(2), f'(2), g(2), and g'(2), and we need to find (fg)'(2).
First, let's use the product rule to find (fg)'(x):
(fg)'(x) = f'(x)g(x) + f(x)g'(x).
Since we're interested in finding (fg)'(2), we can substitute x=2 into the equation:
(fg)'(2) = f'(2)g(2) + f(2)g'(2).
Now we can substitute the given values into the equation:
(fg)'(2) = f'(2)g(2) + f(2)g'(2)
= 2 * 2 + 2 * 2
= 4 + 4
= 8.
So, (fg)'(2) = 8.