Chapter exploration

Techniques of differentiation

Explore

Use the worked example below, then change one input or assumption. Predict which part of the answer must change before calculating.

Explore this related example, then return to the prediction task above.

Step through the layers from the inside out. At x = 5 the inner value is 1.

Start: g(5) = 1

The innermost layer: $g(5)=1$ and $g'(5)=-3$ . This supplies the factor $-3$ .

Marked points at this step, rounded to 6 significant figures.
Point	x	y
g′(5) = −3	1	-3

Ideas to try

Which layer changes the sign? Which changes the size most?