 What is the difference between a partial derivative and a total derivative of a function f? Here the function f depends on x and y, and in both derivatives here we differentiate with respect to x. In the partial derivative written with a curved del, y is independent of x. In the total derivative which is noted with a d, y can depend on x, so the change of the variable x also affects the value of y. Let's make an example. Consider the function 3x squared plus ty. Let's calculate the partial derivative first. To do this, we need to differentiate 3x squared plus differentiate ty. 3x squared, differentiated with respect to x, is 6x. And ty differentiated with respect to x is 0, because we assume in the case of the partial derivative that y is independent of x. Let's now calculate the total derivative of the function. The curved del changes to d. The total derivative of 3x squared is 6x, and the total derivative of ty is no longer 0 because y can depend on x. We can write the factor 2 in front of the derivative. Let's summarize the difference. In the partial derivative the parameters x and y of the function f are independent of each other. In the total derivative on the other hand, x can depend on y, or is in our example, y can depend on x.