Derivative Definition
calculus
Defines the derivative as an instantaneous rate of change.
Math reference
Math Formula Reference
Search structured references across algebra, geometry, trigonometry, calculus, statistics, probability, number theory, and discrete math.
Formula catalog
Browse formulas
22 references found. Results are rendered on the server and limited to 25 per page.
Constant Rule for Derivatives
calculus
The derivative of a constant is zero.
Power Rule for Derivatives
calculus
Differentiates a power of x.
Constant Multiple Rule
calculus
Moves a constant factor outside a derivative.
Sum Rule for Derivatives
calculus
Differentiates a sum term by term.
Product Rule
calculus
Differentiates a product of two differentiable functions.
Quotient Rule
calculus
Differentiates a quotient where g is nonzero.
Chain Rule
calculus
Differentiates a composite function.
Derivative of eˣ
calculus
The natural exponential function is its own derivative.
Derivative of Natural Logarithm
calculus
Differentiates the natural logarithm for positive x.
Derivative of Sine
calculus
Differentiates sine with x in radians.
Derivative of Cosine
calculus
Differentiates cosine with x in radians.
Derivative of Tangent
calculus
Differentiates tangent where it is defined.
Power Rule for Antiderivatives
calculus
Antidifferentiates a power for n not equal to −1.
Integral of 1/x
calculus
Antidifferentiates 1/x on intervals not containing zero.
Integral of eˣ
calculus
The natural exponential is its own antiderivative.
Integral of Sine
calculus
Antidifferentiates sine with x in radians.
Integral of Cosine
calculus
Antidifferentiates cosine with x in radians.
Definite Integral
calculus
Represents accumulated signed change from a to b.
Fundamental Theorem of Calculus
calculus
Evaluates a definite integral using an antiderivative F.
Integration by Substitution
calculus
Rewrites an integral after substituting u = g(x).
Integration by Parts
calculus
Transforms an integral using a product-rule relationship.