Higher Derivatives & Partial DifferentiationRaymund T. de la CruzMAEd - Mathematics

Higher DerivativesIf 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 DerivativeSecond DerivativeThird Derivative

nth Derivative

Higher DerivativesExamples:1. Find the second derivative of Solution:

2. Find the third derivative of Solution:

Higher DerivativesExercise:Find the indicated derivative.

1. Answers:

Partial DifferentiationLetbe 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:1. Find the partial derivatives of Solution:

Partial Differentiation2. Find the partial derivatives of Solution:3. Find the partial derivatives of Solution:

Partial DifferentiationExercise:1. Find the partial derivatives of 2. Find the partial derivatives of 3. Find the partial derivatives of 4. For the given function of find Answers:1.2. ; 3.4.

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