OK, you need to learn this very important lesson: there is no standard for variables. All variables must be defined in the context of the problem; otherwise, we cannot know what they mean or how they can be used.
That being said, I'm guessing, because I've really no clue what your variables are or even if they are variables, that the answer is no. They are not equal.
The RHS looks like the first derivative of the function of x (f'(x)) times the first derivative of another function of x (g'(x)).
But the LHS doesn't appear to be anything if f(x) and g(x) are functions. Perhaps what you meant is [f(x)g(x)]' . And the first derivative of the product of two functions is actually f'(x)g(x) + f(x)g'(x) and not f'(x)g'(x).
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OK, you need to learn this very important lesson: there is no standard for variables. All variables must be defined in the context of the problem; otherwise, we cannot know what they mean or how they can be used.
That being said, I'm guessing, because I've really no clue what your variables are or even if they are variables, that the answer is no. They are not equal.
The RHS looks like the first derivative of the function of x (f'(x)) times the first derivative of another function of x (g'(x)).
But the LHS doesn't appear to be anything if f(x) and g(x) are functions. Perhaps what you meant is [f(x)g(x)]' . And the first derivative of the product of two functions is actually f'(x)g(x) + f(x)g'(x) and not f'(x)g'(x).