Microsoft Math Solver

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.

This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus.

A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory, and calculus.

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let f(x)=g(x)/h(x), where both g and h are differentiable and h(x)≠0. The quotient rule states that the derivative of f(x) is fʼ(x)=(gʼ(x)h(x)-g(x)hʼ(x))/h(x)².