d/dx (f×g)=
(f×g’)+(g×f’)
The product rule states that the derivative of a product of two functions 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. Applying this rule, we can find the derivative of the product of two functions f(x) and g(x) with respect to x as:
d/dx (f(x) × g(x)) = f(x) × d/dx (g(x)) + g(x) × d/dx (f(x))
or
d/dx (f×g) = f × d/dx (g) + g × d/dx (f)
where d/dx (f) and d/dx (g) represent the derivatives of f(x) and g(x) respectively.
So the derivative of the product of two functions f(x) and g(x) with respect to x is the first function times the derivative of the second function, plus the second function times the derivative of the first function.
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