cf'(x)
derivative of a constant times a function
The notation cf'(x) represents the product of a constant c and the derivative of a function f with respect to x. In other words, this can be rewritten as:
cf'(x) = c * d/dx[f(x)]
The result of this expression is a new function whose values are scaled by the constant c and whose slope (or rate of change) is also scaled by c. Note that the derivative of f with respect to x represents how much f changes for a small change in x, so multiplying it by c will cause f to change more rapidly or slowly depending on the value of c.
For example, if f(x) = x^2 and c = 3, then
cf'(x) = 3(2x) = 6x
This means that the slope of the function 6x is three times steeper than that of the original function f(x) = x^2 at every point.
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