Constant factor rule in differentiation

The factor is usually in the Analysis one of the basic rules of the differential calculus, and states that a constant factor remains in differentiating. It follows directly from the definition of the derivative, but can also be regarded as a special case of the product rule.

Rule

If the function is differentiable at the point and a real number, so is the function with

Differentiable at the point, and it is

Example

The function has the derivative function.

Then follows from the control factor, that the function has the derivative function.