calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of...

inverse function. The inverse function is also differentiable, and the inverse function rule expresses its derivative as the multiplicative inverse of...

mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if...

differentiation rules, that is, rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers...

considered above grows very rapidly, its inverse function, f−1, grows very slowly. This inverse Ackermann function f−1 is usually denoted by α. In fact,...

The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution)...

trigonometric functions. The inverse hyperbolic functions are: inverse hyperbolic sine "arsinh" (also denoted "sinh−1", "asinh" or sometimes "arcsinh") inverse hyperbolic...

the usual formula for the quotient rule. Suppose that y = g(x) has an inverse function. Call its inverse function f so that we have x = f(y). There is...

domain. Every surjective function has a right inverse assuming the axiom of choice, and every function with a right inverse is necessarily a surjection...

written logb x, so log10 1000 = 3. As a single-variable function, the logarithm to base b is the inverse of exponentiation with base b. The logarithm base 10...

exponential functions, and their inverses (e.g., arcsin, log, or x1/n). All elementary functions are continuous on their domains. Elementary functions were introduced...

mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f − 1 {\displaystyle f^{-1}}...

differentiable and have a continuous inverse. This is guaranteed to hold if φ is continuously differentiable by the inverse function theorem. Alternatively, the...

to an additive constant, by the condition that the functions' first derivatives are inverse functions of each other. This can be expressed in Euler's derivative...

follows that the composition of two bijections is also a bijection. The inverse function of a composition (assumed invertible) has the property that (f ∘ g)−1...

exponential function is the inverse function of the natural logarithm. The inverse function theorem implies that the natural logarithm has an inverse function, that...

words, an injective function can be "reversed" by a left inverse, but is not necessarily invertible, which requires that the function is bijective. In fact...

calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let h ( x ) = f ( x )...

1694 by the Swiss mathematician Johann Bernoulli. L'Hôpital's rule states that for functions f and g which are defined on an open interval I and differentiable...

implicit function is an inverse function. Not all functions have a unique inverse function. If g is a function of x that has a unique inverse, then the...

product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it...

the function chosen to be dv. An alternative to this rule is the ILATE rule, where inverse trigonometric functions come before logarithmic functions. To...

compute the definite integral of a function when its antiderivative is known; differentiation and integration are inverse operations. Although methods of...

interval I, it has an inverse function, which is a real function with domain f(I) and image I. This is how inverse trigonometric functions are defined in terms...

More generally, a function has a left inverse for function composition if and only if it is injective, and it has a right inverse if and only if it is...

trigonometric functions has a corresponding inverse function, and an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related...

{\displaystyle f} is invertible, and its inverse f − 1 {\displaystyle f^{-1}} is also holomorphic. More, one has by the chain rule ( f − 1 ) ′ ( f ( z ) ) = 1 f...

bullet. In mathematical notation the inverse square law can be expressed as an intensity (I) varying as a function of distance (d) from some centre. The...

In calculus, the power rule is used to differentiate functions of the form f ( x ) = x r {\displaystyle f(x)=x^{r}} , whenever r {\displaystyle r} is...

the implicit function theorem. Inverse function theorem Constant rank theorem: Both the implicit function theorem and the inverse function theorem can...