These functions are applied to tangent functions when making a Mercator [mur-KAY-tur] projection. These functions are listed first, ahead of inverse trigonometric functions, in a common rule of thumb used in integration by parts. The derivatives of these functions are propor
These functions are applied to tangent functions when making a Mercator [mur-KAY-tur] projection. These functions are listed first, ahead of inverse trigonometric functions, in a common rule of thumb used in integration by parts. The derivatives of these functions are proportional to reciprocal functions. An exponent inside one of these functions can be used as a multiplication factor outside them. These functions are the inverse of exponential functions. Name these functions whose “common” type is base 10 and whose “natural” type is base e.