f(x)g'(x) + g(x)f'(x)
The given expression is f(x)g'(x) + g(x)f'(x), which represents the sum of two terms:
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The given expression is f(x)g'(x) + g(x)f'(x), which represents the sum of two terms:
1. f(x)g'(x): This term involves the product of the function f(x) and the derivative of g(x) with respect to x.
2. g(x)f'(x): This term involves the product of the function g(x) and the derivative of f(x) with respect to x.
To simplify this expression, we can apply the product rule of differentiation, which states that the derivative of the product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Using the product rule, we can rewrite the given expression as:
f(x)g'(x) + g(x)f'(x) = (f(x)g(x))’ (applying the product rule)
So, the simplified expression is (f(x)g(x))’.
In other words, f(x)g'(x) + g(x)f'(x) simplifies to the derivative of the product of f(x) and g(x) with respect to x. The product rule allows us to find the derivative of a product without explicitly multiplying the two functions together.
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