Chain Rule
The chain rule differentiates a composition of functions by multiplying derivatives along the composition.
Definition · Example · CSE Use →Calculus
Definitions, examples and Computer Science applications for this mathematics subject.
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Continuity
A function is continuous at a point when its limit there equals its actual function value.
Definition · Example · CSE Use →Definite Integral
A definite integral gives a numerical accumulated value over a fixed interval.
Definition · Example · CSE Use →Derivative
A measure of how a function changes as its input changes; geometrically, the slope of a tangent line.
Definition · Example · CSE Use →Differential Equation
A differential equation relates an unknown function to one or more of its derivatives.
Definition · Example · CSE Use →Differentiate x³ + 2x
Use the power rule. d/dx(x³) = 3x² and d/dx(2x) = 2.Final answer: 3x² + 2.
Definition · Example · CSE Use →Fundamental Theorem of Calculus
The fundamental theorem links differentiation and integration and lets definite integrals be evaluated with antiderivatives.
Definition · Example · CSE Use →Gradient
The gradient is a vector of partial derivatives that points in the direction of steepest increase.
Definition · Example · CSE Use →Indefinite Integral
An indefinite integral represents a family of antiderivatives and includes a constant of integration.
Definition · Example · CSE Use →Integral
A mathematical tool used to accumulate quantities, such as area under a curve.
Definition · Example · CSE Use →Limit
A limit describes the value a function approaches as its input approaches a particular point.
Definition · Example · CSE Use →Optimization
Optimization is the process of finding input values that minimize or maximize an objective function.
Definition · Example · CSE Use →Partial Derivative
A partial derivative differentiates a multivariable function with respect to one variable while holding the others constant.
Definition · Example · CSE Use →Product Rule
The product rule differentiates the product of two functions.
Definition · Example · CSE Use →Quotient Rule
The quotient rule differentiates one function divided by another.
Definition · Example · CSE Use →Taylor Series
A Taylor series represents a smooth function near a point using an infinite polynomial built from derivatives.
Definition · Example · CSE Use →