Higher Derivatives & Partial Differentiation

Differential Calculus

1. Higher Derivatives & Partial Differentiation Raymund T. de la Cruz MAEd - Mathematics

2. Higher Derivatives If y = f (x) is differentiable, its derivative y′ is also called the first derivative of f. If y′ is differentiable, its derivative is called the second derivative of f. If this second derivative is differentiable, then its derivative is called the third derivative of f, and so on. Notation First Derivative   Second Derivative   Third Derivative   nth Derivative  

3. Higher Derivatives Examples: Find the second derivative of Solution:   2. Find the third derivative of Solution:  

4. Higher Derivatives Exercise: Find the indicated derivative.   Answers:  

5. Partial Differentiation Let be a function of two variables. If varies while is held fixed, becomes a function of Then its derivative with respect to is called partial derivative of with respect to and is denoted Similarly, if varies while is held fixed, the partial derivative of with respect to and is denoted   Examples: Find the partial derivatives of Solution:  

6. Partial Differentiation 2. Find the partial derivatives of Solution:   Find the partial derivatives of Solution:  

7. Partial Differentiation Exercise: Find the partial derivatives of Find the partial derivatives of Find the partial derivatives of For the given function of find   Answers: 1. 2. ; 3. 4.  

8. End of Presentation Thank You and God Bless!!!