Section 3.12

Higher Order Derivatives

Since the derivative is itself a function, we can differentiate it again to find acceleration, concavity, and more.

Derivatives of Derivatives

First

Slope
Velocity

Second

Concavity
Acceleration

Third

Jerk
(Change in accel)

Drag the slider to analyze the stack of derivatives.

f(x) Position

f'(x) Velocity

f''(x) Acceleration

Find the second derivative of .

First Derivative

Second Derivative

Differentiate again:

A drone's altitude (in meters) after seconds is given by . Find its velocity and acceleration at .

1. Velocity (First Deriv)

Rate of change of position.

2. Acceleration (Second Deriv)

Rate of change of velocity.

3. Evaluate at t = 3

Velocity

Moving up slowly.

Acceleration

Speeding up (pushing up).