f(x)g'(x) + g(x)f'(x)
The given expression is known as the product rule in calculus
The given expression is known as the product rule in calculus. It helps you find the derivative of the product of two functions.
Let’s break down the notation:
– f(x) and g(x) represent two different functions.
– f'(x) and g'(x) represent the derivatives of these functions with respect to x.
To find the derivative of the product of f(x) and g(x), which is denoted as f(x) * g(x), you need to apply the product rule.
The product rule states that if you have two functions u(x) and v(x), their derivative is given by the formula:
(u(x) * v(x))’ = u'(x) * v(x) + v'(x) * u(x)
In our case, u(x) = f(x) and v(x) = g(x). So, plugging these values into the product rule formula, we have:
(f(x) * g(x))’ = f'(x) * g(x) + g'(x) * f(x)
Hence, the derivative of the product f(x) * g(x) is given by f'(x) * g(x) + g'(x) * f(x).
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