Equation:
Notes:
If a function is expressed as the product of two functions, such as f(x) times g(x) .
[f(x)g(x)]
Take the derivative of the function by taking the derivative of the first function [f(x)], by using the power or chain rule, and multiplying it by the second function [g(x)].
f’(x)g(x)
Next take the derivative of the second function [g(x)], by using the power or chain rule, and multiply it by the first function [f(x)].
g’(x)f(x)
Add the two terms together to get the final derivative.
f’(x)g(x) + g’(x)f(x)
The proof behind the Product Rule:
If a function is expressed as the product of two functions, such as f(x) times g(x) .
[f(x)g(x)]
Take the derivative of the function by taking the derivative of the first function [f(x)], by using the power or chain rule, and multiplying it by the second function [g(x)].
f’(x)g(x)
Next take the derivative of the second function [g(x)], by using the power or chain rule, and multiply it by the first function [f(x)].
g’(x)f(x)
Add the two terms together to get the final derivative.
f’(x)g(x) + g’(x)f(x)
The proof behind the Product Rule:
Example Problems
Here is a video for extra help:
www.educreations.com/lesson/view/product-rule/41933327/?s=hU2Oue&ref=link
www.educreations.com/lesson/view/product-rule/41933327/?s=hU2Oue&ref=link