d/dx[C x f(x)]=
cf'(x)
To find the derivative of C x f(x) with respect to x, we use the product rule of differentiation, which states that the derivative of the product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function. Mathematically, this can be expressed as:
d/dx[C x f(x)] = C x d/dx[f(x)] + f(x) x d/dx[C]
Since C is a constant, its derivative with respect to x is zero. Therefore, we can simplify the above expression as:
d/dx[C x f(x)] = C x d/dx[f(x)]
So the derivative of C x f(x) with respect to x is equal to C times the derivative of f(x) with respect to x.
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