All Tools

Function Graph Explorer

Plot functions, explore their properties, and see step-by-step derivative analysis. Updated in real-time.

Functions

f
g
h
Display:

Properties

Enter a function and click Graph to see properties.

Quick Reference

Derivative Rules

Power Rule
ddx[xn]=nxn−1\frac{d}{dx}[x^n] = nx^{n-1}
Product Rule
ddx[f⋅g]=f′g+fg′\frac{d}{dx}[f \cdot g] = f'g + fg'
Chain Rule
ddx[f(g(x))]=f′(g(x))⋅g′(x)\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)

Trig Derivatives

ddx[sin⁡x]=cos⁡x\frac{d}{dx}[\sin x] = \cos x
ddx[cos⁡x]=−sin⁡x\frac{d}{dx}[\cos x] = -\sin x
ddx[tan⁡x]=sec⁡2x\frac{d}{dx}[\tan x] = \sec^2 x
ddx[ex]=ex\frac{d}{dx}[e^x] = e^x
ddx[ln⁡x]=1x\frac{d}{dx}[\ln x] = \frac{1}{x}

Graph Features

Roots Where f(x)=0f(x) = 0. The function crosses the x-axis.
Extrema Where f′(x)=0f'(x) = 0. Local maxima or minima.
Inflection Where f′′(x)=0f''(x) = 0. Concavity changes.

Increasing: f′(x)>0f'(x) > 0  |  Decreasing: f′(x)<0f'(x) < 0

Interval Notation

Open interval (a,b)(a, b) Excludes endpoints.
Closed interval [a,b][a, b] Includes endpoints.
Unbounded (−∞,a)(-\infty, a) or (b,∞)(b, \infty)
Union A∪BA \cup B Combines intervals.
Example (−∞,−1)∪(2,∞)(-\infty, -1) \cup (2, \infty) means all xx less than −1-1 or greater than 22.