d/dx (fg)
fg’ + gf’
Using the product rule, the derivative of f(x) multiplied by g(x) with respect to x is given by:
d/dx (f(x)g(x)) = f(x) d/dx(g(x)) + g(x) d/dx(f(x))
Therefore, for d/dx(fg), we let f(x) = f and g(x) = g, such that:
d/dx(fg) = f d/dx(g) + g d/dx(f)
= f d/dx(g) + g d/dx(f)
So, we simply compute the derivatives of f(x) and g(x) with respect to x and substitute them into the above equation, giving:
d/dx(fg) = f d/dx(g) + g d/dx(f)
= f * g’ + g * f’
where f’ and g’ denote the derivatives of f(x) and g(x) with respect to x, respectively.
Therefore, the derivative of f(x) multiplied by g(x) with respect to x is f multiplied by g prime plus g multiplied by f prime.
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