Defination of Partial Differentiation
If f is a function of several variables , then the derivative of f w.r.t. keeping other variables constant is called partial derivative of f w.r.t. and is denoted by or by and is defined as:
provided the limit exists.
3. if f=f(x,y) and partial derivates are continuous then
4. if f=f(x,y), then . if g=g (x,y,z), then .
if f=f(x,y) and , then:
If f is a homogenous function of x and y of degree n, then it may be put in the form .
If f is a homogenous function of x and y of degree n , then
Deduction: From this, we get some important results as follows:
Note: The above results are very important for doing problems.
(1) if , then degree of f is and f is homogenous.
Then is homogenous degree 3 -4 = -1.
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