What is meant by partial derivative?

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.

Why is it called a partial derivative?

Indication that the input of a multivariable function can change in many directions. Neither one of these derivatives tells the full story of how our function f ( x , y ) f(x, y) f(x,y)f, left parenthesis, x, comma, y, right parenthesis changes when its input changes slightly, so we call them partial derivatives.

What is difference between derivative and partial derivative?

The total derivative is a derivative of a compound function, just as your first example, whereas the partial derivative is the derivative of one of the variables holding the rest constant.

How do you find the partial derivative?

Example 1

1. Let f(x,y)=y3x2. Calculate ∂f∂x(x,y).
2. Solution: To calculate ∂f∂x(x,y), we simply view y as being a fixed number and calculate the ordinary derivative with respect to x.
3. For the same f, calculate ∂f∂y(x,y).
4. For the same f, calculate ∂f∂x(1,2).

Why partial differentiation is important?

Partial differentiation is used to differentiate mathematical functions having more than one variable in them. So partial differentiation is more general than ordinary differentiation. Partial differentiation is used for finding maxima and minima in optimization problems.

How is partial derivative determined?

Solution: To calculate ∂f∂x(x,y), we simply view y as being a fixed number and calculate the ordinary derivative with respect to x. Then, the partial derivative ∂f∂x(x,y) is the same as the ordinary derivative of the function g(x)=b3x2. Using the rules for ordinary differentiation, we know that dgdx(x)=2b3x.