Скачать или смотреть Key Differences Explained partial vs total derivative | total derivative | partial derivatives

Key Differences Explained partial vs total derivative | total derivative | partial derivatives

Understand the difference between partial and total derivatives with clear examples. Learn how they apply to multivariable functions and why they matter in calculus and real-world problems. partial derivatives engineering mathematics | partial derivatives engineering mathematics | partial derivatives | partial derivatives engineering mathematics one shot | partial derivative equations | partial derivative btech 1st year total derivative, partial derivatives, total vs partial derivative

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 2y". Let's calculate the partial derivative first.

To do this, we need to differentiate "3x squared" Plus differentiate "2y". "3x squared" differentiated with respect to "x" is "6x". And "2y" differentiated with respect to "x" is zero, 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 a "d". The total derivative of "3x squared" is "6x" and the total derivative of "2y" is no longer zero, 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, as in the example, "y can depend on x".

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