Find (fg)'(1)
if f(1)=1, g(1)=2,f'(1)=3, g'(1)=-3
To find (fg)'(1), we will use the product rule, which states that the derivative of the product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Let's denote f(x) as the first function and g(x) as the second function.
The product rule states:
(fg)'(x) = f'(x) * g(x) + f(x) * g'(x)
To find (fg)'(1), we substitute the given values into the product rule formula:
(fg)'(1) = f'(1) * g(1) + f(1) * g'(1)
Substituting the given values:
(fg)'(1) = 3 * 2 + 1 * (-3)
Evaluating the expression:
(fg)'(1) = 6 - 3
Simplifying gives us:
(fg)'(1) = 3
Therefore, (fg)'(1) equals 3.