search
search
user.png
vertical menu
Teacher Tools > Lesson Plans > Lesson Plans By Subject > Math Lesson Plans

Higher order derivatives

Higher order derivatives preview
Higher order derivatives preview
Higher order derivatives video preview 2
display-video

Look Inside · 10 pages

Lesson cover titled 'Higher order derivatives' with an objective to find second, third, or higher derivatives
Cover and learning objective for the calculus lesson
Opening lesson example differentiates f(x) = 2x⁵ − 3x³ + 5x − 4 repeatedly, through the fifth derivative
Opening example: first through fifth derivatives
Definition slide explains second derivatives as the rate of change of the gradient, using f″(x) and d²y/dx²
Second derivative definition and notation
Motion application slide links position, velocity, and acceleration through s′(t) = v(t) and a(t) = s″(t)
Motion application of the second derivative
Notation slide introduces third derivatives as f‴(x) or d³y/dx³ and higher derivatives as f⁽ⁿ⁾(x) or dⁿy/dxⁿ
Notation for third and higher derivatives
Worked example slide finds the first three derivatives of y = 3x⁵ + 4/x² by rewriting the reciprocal term
Worked example using negative exponents
Worked example slide finds f′(x) and f″(x) for f(x) = 3√x + 1/(2√x) by rewriting roots as fractional powers
Worked example using fractional exponents
Mixed-function example begins with f(x) = sin(3x) + e⁻²ˣ + ln(7x) and works out its first derivative
Mixed-function example, step 1: first derivative
Mixed-function example continues by differentiating again to obtain f″(x) = −9 sin(3x) + 4e⁻²ˣ − x⁻²
Mixed-function example, step 2: second derivative
Mixed-function example continues to the third derivative, giving f‴(x) = −27 cos(3x) − 8e⁻²ˣ + 2x⁻³
Mixed-function example, step 3: third derivative
Attributes
Subject

Math, Calculus

Grades

Grade 12

Types

Teacher Tools, Lesson Plans

File

Microsoft PowerPoint

Editable
No
Author
Maths Support Centre
Rating
Add To Collection
Add to collection Add to collection

About This Product

PowerPoint presentation, 12 slides explaining how to find second, third or higher-order derivatives.

What's Included

PowerPoint presentation, 12 slides

Resource Tags

calculus derivative second derivatives third derivatives higher order derivatives

0 Reviews

Explore related searches
you may also like...

Check out these other great products

Derivatives of Trig Functions – 13-Slide Lesson
Derivatives of Trig Functions – 13-Slide Lesson
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product
Introduction to derivative
Introduction to derivative
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product
Derivatives of Inverse Trig Functions – PowerPoint
Derivatives of Inverse Trig Functions – PowerPoint
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product
Derivative of exponential and logarithmic functions
Derivative of exponential and logarithmic functions
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product
Basic rules of derivative
Basic rules of derivative
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product
Differentiation: The product rule
Differentiation: The product rule
Teacher Tools, Lesson Plans
Add to collection Add to collection
Download product