· Problems based on Partial Derivatives
· Problems based on Euler`s Theorem
· Problems based on Total Derivatives-Differentiation of Implicit Function
· Problems based on Jacobian
· Problems based on Taylor`s and Laurent Series
· Problems based on Maxima and Minima for Functions of Two Variables
· Problems based on Lagrangian Multiplier

**Functions of several Variables**

·** Problems based on Partial Derivatives**

**· Problems based on Euler`s Theorem**

**· Problems based on Total Derivatives-Differentiation of Implicit Function**

**· Problems based on Jacobian**

**· Problems based on Taylor`s and Laurent Series**

**· Problems based on Maxima and Minima for Functions of Two Variables**

**· Problems based on Lagrangian Multiplier**

**Partial Derivatives**

**Partial Derivatives:** Let z=f(x,y) be a function of two Variables x and y, If we keep y as a constant and Vary x alone , then z is a function of x only ,

The derivative of z w.r.to x, treating y as a constant is called the partial derivatives w.r.to x and it is denoted by the symbols

**Successive Partial Differentiation:**

**Euler`s Theorem for Homogeneous Function**

**Euler`s Theorem:** If u be a homogeneous function of degree n an x and y then

**Total Derivatives-Differentiation of Implicit Function**

**Total Derivative:**

**Maxima and Minima and Lagrangian Multiplier**

** Defn: Maximum Value**

if f(a,b) is a maximum value of (x,y) if their exists some neighbourhood of the point (a,b) such that for every point (a+h,b+k) of the neighbourhood

f(a,b)>f(a+h,b+k)

** Defn: Minimum Value**

if f(a,b) is a maximum value of (x,y) if their exists some neighbourhood of the point (a,b) such that for every point (a+h,b+k) of the neighbourhood

f(a,b)<f(a+h,b+k)

** Defn: Extremum Value**

if f(a,b) is said to be an extremum value o if f(a,b) it is maximum or minimum

** Defn: Lagrangian Multiplier**

Suppose we require to find the maximum and minimum values of (x,y,z) where x,y,z are subject to a constraint equation g(x,y,z)=0

We define a function F(x,y,z) = f(x,y,z) + λg(x,y,z) where λ is called Lagrangian Multiplier which is independent of x,y,z.

**Problems:**

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