Partial Implicit Differentiation Concepts

Partial Implicit Differentiation Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

CCSS
HSF.TF.B.7

Standards-aligned

Created by

Olivia Brooks

FREE Resource

Standards-aligned

CCSS.HSF.TF.B.7
The video tutorial covers partial implicit differentiation, starting with a brief introduction to the concept. It explains how to find partial derivatives of functions defined implicitly and provides three examples. The first example demonstrates basic partial derivative calculations, the second focuses on simplifying fractions, and the third involves trigonometric functions. The video emphasizes the importance of rewriting equations in the correct form and highlights common pitfalls in simplification.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the basic form of an implicit equation used in partial implicit differentiation?

F(x, y) = 1

F(x, y, z) = 0

F(x, y) = 0

F(x, y, z) = 1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what is the common factor used to simplify the partial derivative of z with respect to y?

3

4

2

5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the denominator for the partial derivative of z with respect to x in the second example?

2z

3x

4y

6z

Tags

CCSS.HSF.TF.B.7

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what is the common factor used to simplify the partial derivatives?

3

2

5

4

Tags

CCSS.HSF.TF.B.7

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step when dealing with an equation involving trigonometric functions?

Differentiate directly

Set the equation equal to zero

Simplify the equation

Factor out constants

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the trigonometric example, what is the derivative of sine(yz) with respect to z?

cos(yz) * y

sin(yz) * y

cos(yz) * z

sin(yz) * z

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the partial derivative of z with respect to x in the trigonometric example?

y cos(xy) + z cos(zx)

y cos(xy) + x cos(zx)

x cos(xy) + y cos(yz)

z cos(xy) + x cos(zx)

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