INVESTIGATION MODE
Instructions
Use the function editor in the workspace to select a function. Move the x slider to explore, then click Capture to record data.
f(x) = x²
Recorded Data
x f(x) f'(x) Type
Move x slider and click Capture to record
Live Graph
Record 2+ data points to see the graph
What To Explore
Where is f'(x) = 0? What happens to f(x) there?
When f'(x) > 0, is f(x) increasing or decreasing?
Try sin(x): where is the derivative exactly 0?
EQUATION LAB — Differentiation Rules
Symbols
f(x)Original function
f'(x)Derivative — instantaneous rate of change
xInput variable
nPower exponent
mSlope of tangent line
Differentiation Rules
Power Rule
If f(x) = xⁿ, the derivative is n times x to the power (n−1). Bring down the exponent, reduce by 1.
Chain Rule (composite)
Derivative of a composite function. Differentiate outer, multiply by derivative of inner.
Tangent Line
The red line has slope equal to f'(x) at the chosen point. It just touches the curve.
Current Function
Derivative

Desmos — Differentiation Explorer