Reciprocal rule

The Reziprokenregel used to derive mathematical functions of the form

If the function of an interval in the real or complex numbers at the site with differentiable, then the function is differentiable at the point and according to the chain rule for the derivative:

The Reziprokenregel thus reads as follows in short notation:

The Reziprokenregel can also be regarded as a special case of the quotient rule with.

Example

The derivative of the function

Is calculated at all points at which is according to the above Reziprokenregel to

Because the cosine function is the derivative of the sine function.