d/dx [uv]
derivative of the product of two functions, UV, is equal to the first function, U, multiplied by the derivative of the second function, d/dx[V], plus the second function, V, multiplied by the derivative of the first function, d/dx[U].
The product rule states that the derivative of a product of two functions, u(x) and v(x), is the sum of the first function times the derivative of the second function plus the second function times the derivative of the first function.
So, applying the product rule to d/dx [uv], we get:
d/dx [uv] = u(x) * d/dx[v(x)] + v(x) * d/dx[u(x)]
Therefore, the derivative of the product of two functions, UV, is equal to the first function, U, multiplied by the derivative of the second function, d/dx[V], plus the second function, V, multiplied by the derivative of the first function, d/dx[U].
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