Applied Calculus: UNIT II: Functions of Several Variables

Partial derivatives: Problems under type-2

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Explanation, Formula, Equation, Example and Solved Problems - Partial derivatives: Problems under type-2

PROBLEMS UNDER TYPE 2

If u = f(x,y) and x and y is connected by a relation ϕ(x, y) = 0, then

Example 26. Find du/dx if u = tan(x² + y²), where a²x² + b²y² = c².

Solution: Given u = tan(x² + y²)

Example 27. Find du/dx if u = x²y, where x² + xy + y² = 1.

Solution: Given u = x²y

Example 28. If u = xlogxy where x³+ y³ + 3xy = 1, find du/dx.

Solution: We have f(x, y) = x³+ y³ + 3xy ‒ 1

du/dx = 1+ logxy ‒ x(x² + y)/y(y² + x) [By (i)]

Applied Calculus: UNIT II: Functions of Several Variables : Tag: Applied Calculus : - Partial derivatives: Problems under type-2

Home | Department: Ist Year | Subject: Applied Calculus |

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Applied Calculus: UNIT II: Functions of Several Variables

Functions of Several Variables: Introduction

Partial derivatives

Partial derivatives: Total derivatives

Partial derivatives: Problems under type-1

Partial derivatives: Problems under type-2

Partial derivatives: Problems under type-3

Partial derivatives: Problems under type-4

Maxima and Minima without Constraints

Application Problems in Engineering - Functions of Several Variables

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