Learn Partial Derivatives

Let z be a function of x and y such that z = f(x,y). z is therefore a function of two variables x and y.

If we keep y as constant and vary z alone, then a is a function of x only. The derivative of z with respect to x, treating y as constant is called the partial derivative of z with respect to x and is denoted by one of the partial derivative symbols listed below:

,provided this limit exists.

Similarly the derivative of z with respect to y, keeping x as constant, is called the partial derivative of z with respect to y and is denoted by one of the following partial derivative symbol:

Similarly if z is a function of three or more variables, x_1, x_2, …… x_n, then partial derivative of z with respect to x_1, is obtained by differentiating z with respect to x_1, keeping all other variables constant and is denoted by dz/dx_1.

Partial derivative examples: