Enter the original functions and their derivatives into the calculator to determine the derivative of the product of two functions.
Leibniz Rule Formula
The following formula is used to calculate the derivative of the product of two functions using the Leibniz Rule.
(f*g)' = f' * g + f * g'
Variables:
- (f*g)’ is the derivative of the product of function f and function g f’ is the derivative of function f g is the original function g f is the original function f g’ is the derivative of function g
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 a Leibniz Rule?
The Leibniz Rule, also known as the product rule, is a fundamental theorem in calculus that provides a formula to differentiate the product of two functions. Named after Gottfried Wilhelm Leibniz, this rule states that the derivative of the product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function. It is a key tool in differential calculus and is used to simplify the process of finding derivatives.
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’.
- Next, determine the product of function f and function g, denoted as f * g.
- Next, determine the product of the derivative of function f and function g, denoted as f’ * g.
- Finally, calculate the derivative of the product of function f and function g, denoted as (f*g)’. This can be done by adding the results from steps 3 and 4, i.e., (f’ * g) + (f * g’).
Example Problem:
Use the following variables as an example problem to test your knowledge:
f’ = 2
g = x^2
f = 3x
g’ = 2x
