Formula

Tags

• Differential calculus
• Derivative
• Definition of the derivative
• Derivative formula
• Limit

Detail

Explore the idea

Variables

• $x$Independent variable
• $h$Increment in the derivative definition
• $f$Function
• $f'$Derivative of $f$

Frequently asked questions

What does the derivative measure at a point?

The derivative $f'(a)$ is the slope of the tangent to the graph of $f$ at $x=a$, and also the limit of the difference quotient as $h\to0$.

Also known as

• derivative
• slope
• difference quotient

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

  $$G(x)=\int_a^x f(t)\,dt,$$
  Open formulaOpen in section

• Related

  Formula

  $$y-f(a)=f'(a)(x-a)$$
  Open formulaOpen in section

• Related

  Formula

  $$f'(a)=\lim_{x\to a}\frac{f(x)-f(a)}{x-a}$$
  Open formulaOpen in section