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Differentiable function – Mathematical function whose derivative exists; Differential of a function – Notion in calculus; Differentiation of integrals – Problem in mathematics; Differentiation under the integral sign – Differentiation under the integral sign formula; Hyperbolic functions – Collective name of 6 mathematical functions
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. Minkowski's question mark function: Derivatives vanish on the rationals. Weierstrass function: is an example of continuous function that is nowhere differentiable
Dirac delta function; Solution methods. ... This list presents differential equations that have received specific names, area by area. Mathematics
Derivative; Notation. Newton's notation for differentiation; Leibniz's notation for differentiation; Simplest rules Derivative of a constant; Sum rule in differentiation
for the nth derivative. When f is a function of several variables, it is common to use "∂", a stylized cursive lower-case d, rather than "D". As above, the subscripts denote the derivatives that are being taken. For example, the second partial derivatives of a function f(x, y) are: [6]
Here is a particular example, the derivative of the squaring function at the input 3. Let f(x) = x 2 be the squaring function. The derivative f′(x) of a curve at a point is the slope of the line tangent to that curve at that point. This slope is determined by considering the limiting value of the slopes of the second lines.
Arithmetic function: A function from the positive integers into the complex numbers. Analytic function: Can be defined locally by a convergent power series. Quasi-analytic function: not analytic, but still locally determined by its derivatives at a point. Differentiable function: Has a derivative.