Leibniz Rule Calculator - Calculator Academy

Enter the original functions and their derivatives into the calculator to determine the derivative of the product of two functions.

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Leibniz Rule Formula

The following formula is used to calculate the derivative of the product of two functions using the Leibniz Rule (product rule).

(f*g)' = f' * g + f * g'

Variables:

(f·g)' is the derivative of the product of f and g.
f is the original function f(x).
g is the original function g(x).
f' is the derivative of f with respect to the variable.
g' is the derivative of g with respect to the variable.

To calculate the derivative of the product of two functions, first find the derivative of function f and multiply it by function g. Then, multiply function f by the derivative of function g. Add these two results together to get the derivative of the product of the two functions.

What is the Leibniz Rule?

The Leibniz rule is commonly used to refer to the product rule in calculus, which provides a formula to differentiate the product of two functions. It is named after Gottfried Wilhelm Leibniz. In a broader sense, “Leibniz rule” can also refer to the generalized (nth-derivative) product rule.

How to Calculate Leibniz Rule?

The following steps outline how to calculate the Leibniz Rule:

First, determine the derivative of function f, denoted as f'.
Next, determine the derivative of function g, denoted as g'.
Compute the product of the derivative of function f and function g, denoted as f' * g.
Compute the product of function f and the derivative of function g, denoted as f * g'.
Finally, calculate the derivative of the product, denoted as (f*g)'. This is done by adding the results from steps 3 and 4: (f' * g) + (f * g').

Example Problem:

Use the following variables as an example problem to test your knowledge:

f' = 3

g = x^2

f = 3x

g' = 2x