The Chain Rule Activating Strategy

Presentation

•

Mathematics

•

12th Grade

•

Practice Problem

•

Medium

•

CCSS

6.NS.B.3, HSF.IF.A.2

Standards-aligned

Patrick Antonucci

Used 3+ times

FREE Resource

6 Slides • 9 Questions

How is Lindt Chocolate Made?

The process of making chocolate is quite involved and includes multiple steps. In large chocolate factories, this process has many automated components and uses an assembly line. At each station, a single component of the process is completed before it is sent off to the next station in the chain.

Reorder

The steps for making chocolate bars are jumbled below.

Put them in the correct order by numbering each step from 1 to 4.

Roasting and crushing the beans

Mixing in other dry ingredients (milk powder, vanilla, sugar)

Conching and tempering (heating and smoothing out the chocolate paste)

Packaging

Labeling

List the inputs and outputs at each step in the chocolate making process.

Drag labels to their correct position on the image

Paste

Crushed Beans

Chocolate

Beans

Lindt Package

Notice that the output of one step becomes the input of the next step

Here is the solution to the previous slide

Math Response

We are going to use the assembly line approach to analyze a complex function with multiple parts. Let’s look at the function $y=\sin\left(x^2-3\right)$

The raw material is our input, or independent variable. What is the independent variable of this function?

Type answer here

Deg^°

Rad

Reorder

Imagine evaluating $y=\sin\left(x^2-3\right)$ at x=5.

What happens first in the assembly line?

What happens next?

Put the steps below in the correct order.

Substitute 5 in for x.

Square it

Subtract 3 from it

Take the sine of it

Math Response

To find the derivative of this function, we will need to consider how each link in the chain contributes to the end product.

If $\nabla=x^2-3$ , what is $\frac{d\nabla}{dx}?$

Type answer here

Deg^°

Rad

Fill in the Blanks

Plugging $\nabla=x^2-3$ back into our original function, we see that $y=\sin\nabla$ .

What is $\frac{dy}{d\nabla}?$

Fill in the Blanks

Now to get our final product we multiply the two answers from the previous steps.

So $\frac{d\nabla}{dx}\cdot\frac{dy}{d\nabla}$ .

What does this product simplify to if we treat it like multiplying fractions?

Here are the main takeaways from this activity:

Multiple Choice

Your turn:

Differentiate using the Chain Rule.

Then select the correct answer.

-2sin(2x)

-sin(2x)

sin(2x)

2sin(2x)

2sin(x)

Math Response

If $y=\left(x^2-4\right)^5$

Then $\frac{dy}{dx}=$

Type answer here

Deg^°

Rad

Great job!!!
You finished the Chain Rule Activating Strategy

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