Formula

Tags

• Differential calculus
• Derivative
• Derivative formula
• Rule
• Chain rule

Explore the idea

Variables

• $x$Independent variable
• $f$Function
• $g$Second function or inner composition
• $f'$Derivative of $f$
• $dx$Differential of $x$

Frequently asked questions

When do I use the chain rule?

When differentiating a composition $f(g(x))$: the derivative is $f'(g(x))\cdot g'(x)$. Also in Leibniz notation: $dy/dx=(dy/du)(du/dx)$.

Also known as

• regla de la cadena
• chain rule
• composition

Related topics

• Chain rule

Related formulas

• Related

  More generally, by the chain rule:

  $$\frac{d}{dx}\int_a^{g(x)}f(t)\,dt=f(g(x))g'(x).$$
  Open formulaOpen in section

• Related

  Formula

  $$\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$$
  Open formulaOpen in section

• Related

  Formula

  $$(fg)'=f'g+fg'$$
  Open formulaOpen in section