what are the rules of partial differentiation . Explain in brief.
Answers
The rules of partial differentiation follow exactly the same logic as univariate differentiation. The only difference is that we have to decide how to treat the other variable. Recall that in the previous section, slope was defined as a change in z for a given change in x or y, holding the other variable constant.
Answer:
Suppose, we have a function f(x, y), which depends on two variables x and y, where x and y are independent of each other. Then we say that the function f partially depends on x and y. Now, if we calculate the derivative of f, then that derivative is known as the partial derivative of f. If we differentiate the function f with respect to x, then take y as a constant and if we differentiate f with respect to y, then take x as a constant.
Partial Derivative Symbol
In mathematics, the partial derivative of any function having several variables is its derivative with respect to one of those variables where the others are held constant. The partial derivative of a function f with respect to the differently x is variously denoted by f’x,fx, ∂xf or ∂f/∂x. Here ∂ is the symbol of the partial derivative.
Example: Suppose f is a function in x and y then it will be expressed by f(x, y). So, the partial derivative of f with respect to x will be ∂f/∂x keeping y as constant. It should be noted that it is ∂x, not dx. ∂f/∂x is also known as fx.
Partial Derivative Formula
If f(x,y) is a function, where f partially depends on x and y and if we differentiate f with respect to x and y then the derivatives are called the partial derivative of f. The formula for partial derivative of f with respect to x taking y as a constant is given.