Constant Multiple Rule Derivative Math

For instance the derivative of 𝑓 𝑥 5𝑥 is 𝑓 𝑥 5.

Constant multiple rule derivative math. The derivative of any linear function is a constant meaning no matter what 𝑥 value you choose the derivative is always the same. Therefore g x k. Constant multiple rule of derivatives proof math wiki. This is 5 no matter what 𝑥 is.

The constant multiple rule for any real number if is a differentiable function with derivative then. In words this rule says that the derivative of a constant times a function is the constant times the derivative of the function. Let k be a constant then the product of constant k and the function f x is called the constant multiple function which is written in product form as k. To repeat bring the power in front then reduce the power by 1.

Ap is a trademark registered and owned by the college board which was not involved in the production of and does not endorse this site is a trademark registered and owned by the college board which was not involved in the production of and does not endorse this site. Derivative rules constant rule constant multiple rule power rule sum rule difference rule product rule quotient rule chain rule exponential functions logarithmic functions trigonometric functions inverse trigonometric functions hyperbolic functions and inverse hyperbolic functions with video lessons examples and step by step solutions. Find the derivative of constant multiple function take the constant multiple function is denoted by g x. Dfrac d dx big kf x big k dfrac d dx big f x big that is text for m x kf x quad m x kf x.

The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the derivative. That s all there is to it. F x 5 is a horizontal line with a slope of zero and thus its derivative is also zero. This video is unavailable.

Add new page. These include the constant rule power rule constant multiple rule sum rule and difference rule. Informally we say that the slope of a line is constant everywhere.