icon-Mathe Differentiation Rules

Derivatives

d d x Const. = 0

d d x x = 1

d d x xn = nxn-1

Derivative of trigonometric functions

d d x sin(x) = cos(x)

d d x cos(x) = -sin(x)

d d x sin(kx) = kcos(kx)

d d x cos(kx) = -ksin(kx)

d d x tan(x) = d d x sin(x) cos(x) = 1 cos2(x)

Derivation exponential and logarithmic functions

d d x ex = ex

d d x ln(x) = 1x

d d x loga(x) = 1xloga(e)

Derivation Calculator

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e(x)⋅sin(x)⋅cos(x)

Differential Calculus

Differentiation Rules

The following are the most important differentiation rules described and illustrated by examples.

  • Factor Rule
  • Sum rule
  • Product Rule
  • Quotient Rule
  • Chain Rule

Factor rule and Sum rule

Ableitungsregel-1

Examples for Factor rule and Sum rule

Ableitungsregel-1

Product rule

Ableitungsregel-2

Examples for Product rule

Ableitungsregel-1
Ableitungsregel-1

Quotient rule

Ableitungsregel-3

Example for Quotient rule

Ableitungsregel-1

Chain rule

Ableitungsregel-4

Example for Chain rule

Ableitungsregel-1

Mixed differentiations

Ableitungsregel-4 Ableitungsregel-4 Ableitungsregel-4