A double slope, more formally referred to as a double derivative, is a measure of the rate of change of the slope. A common example of a double slope is the determination of acceleration from the position function. Taking the first derivative of the position function shows the rate of change, specifically the velocity, of a body through space. Taking the second derivative, the double slope, shows the rate at which this velocity is changing, otherwise known as acceleration. The process of determining double slopes is known as taking higher order derivatives and is performed throughout all sciences.
Instructions
-
-
1
Convert the equation to function notation. For example, y = x^4 becomes f (x) = x^4.
-
2
Take the first derivative of the function. Using the general power rule for derivatives, f ' (x) = 4x^3. Note the apostrophe after the "f"; this new function is spoken as "f prime of x."
-
-
3
Take the derivative of the newly derived function. Again, using the general power rule for derivatives, the derivative of f ' (x) = 4x^3 is equal to f ' ' (x) = 12x^2. This new function is spoken as "f double prime of x." This final result is the double slope of the original function.