Understanding Differentials

This video tutorial explains how to determine differential Y through three examples. It begins with an introduction to the concept and formula of differential Y, highlighting its role in approximating changes in functions. The video then provides step-by-step examples, including basic derivatives, the application of the chain rule, and handling composite functions. Each example demonstrates the process of finding the derivative of a given function and calculating differential Y.

What is the primary purpose of determining differential Y?

• To determine the maximum value of a function

• To solve complex equations

• To approximate the change in Y of a function

• To find the exact value of a function

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CCSS.HSF.IF.B.6

CCSS.8.F.B.4

What is the formula for differential Y in terms of derivatives?

• DY = F(X) + DX

• DY = F PRIME OF X x DX

• DY = F PRIME OF X + DX

• DY = F(X) x DX

In the first example, what is the derivative of the function given?

• 15X SQUARED - 14X + 4

• 10X SQUARED - 14X + 4

• 15X SQUARED - 10X + 4

• 15X CUBED - 14X + 4

What rule is applied in the second example to find differential Y?

• Chain Rule

• Power Rule

• Quotient Rule

• Product Rule

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CCSS.HSF-BF.A.1C

In the second example, what is the inner function U?

• 2X + 5

• 3X + 5

• 2X + 3

• X + 5

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CCSS.HSN.RN.A.2

What is the exponent of U in the second example?

• 3/2

• 2/3

• 1/3

• 1/2

In the third example, what is the outer function's exponent?

• 2/5

• 4/5

• 3/5

• 1/5

What is the derivative of the inner function in the third example?

• 12X to the 4th

• 9X to the 3rd

• 12X to the 3rd

• 9X to the 4th

What is the denominator in the expression for differential Y in the third example?

• 3X to the 4th minus 2 to the 1/5

• 3X to the 4th minus 2 to the 4/5

• 3X to the 4th minus 2 to the 3/5

• 3X to the 4th minus 2 to the 2/5

What is the final step in determining differential Y in the third example?

• Divide by DX

• Multiply by DX

• Add DX

• Subtract DX