The derivative is a slope. You will be using a pencil as a tangent to a curve. As you move the tangent from the left to the right along the curve, you will also describe in words the slope of that tangent which is also the slope of the curve at that point. So, as you move the tangent pencil and state the slopes aloud, you are taking the derivative of the curve.
This page permits the user to choose between a hands-on, pencil & paper use, and a digital presentation.
1. Sharpened Pencil
2. One of these pictures of graphs of the trig functions:
To take the first derivative, use a pencil. Use the middle point of a pencil as a tangent point and point the pencil to the right, the greater x values. Trace the curve, stating the derivative (slope of the tangent) as you do.
Use the stated derivatives (slopes) to describe the curve which is the derivative functions.
For example, TAKE THE DERIVATIVE OF THE SINE.
What's the function?
The derivative of the sine is the cosine.
Two methods for taking the second derivative, the slope of the derivative, are suggested. EITHER repeat the above method using the cosine as the original function, OR, use the movement of the PENCIL POINT and the sine function to compute the second derivative of the sine, d2[sin(x)]/dx2.