From the course: Machine Learning Foundations: Calculus

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The power rule on a function chain

The power rule on a function chain - Python Tutorial

From the course: Machine Learning Foundations: Calculus

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The power rule on a function chain

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- [Instructor] The chain rule enabled us to differentiate a function that is composed of two or more functions. Let's look at the rule that combines together the power rule and the chain rule. So, the power rule on a function chain is going to help us calculate the derivatives of nested functions, where we have the outside function, which is a power function, and the inside function, which is some other kind of function. The formula for power rule on a function chain is the following. Let's see how to use it on a simple example. Y equals 4X minus 1 to the power of 3. First, we have to identify our inner function. In our case, it's simple. F of X equals 4X minus 1, and the outside function is raised to the power of 3. Basically, we are looking at our function as the composition of the inner function and the outer function. Based on our rule, F prime is going to be equal to exponent 3, pulled out in front of,…

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