Let's explore multiple strategies to tackle derivatives involving both the product and chain rules. We start by applying the chain rule first, then the product rule.

Unit 7: Product, quotient, & chain rules About this unit Covered basic differentiation? Great! Now let's take things to the next level. In this topic, you will learn general rules that tell us how to differentiate …

We explore the connection between the quotient rule, product rule, and chain rule in calculus. Rather than memorizing another rule, we see how the quotient rule naturally emerges from applying the …

In the cases where the product rule and chain rule methods are both possible to use, the results will be the same. In some cases, it would be extremely inefficient to use the product rule and much more …

Usually, the only way to differentiate a composite function is using the chain rule. If we don't recognize that a function is composite and that the chain rule must be applied, we will not be able to …

The chain rule tells us how to find the derivative of a composite function. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) we can now differentiate.

The chain rule tells us how to find the derivative of a composite function. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) we can now differentiate.

We also emphasize the importance of fully applying the Chain Rule, and avoid the pitfall of taking the derivative of the outer function with respect to the derivative of the inner function.

So, what would be the difference between using Sal's method here of the product rule, and leaving one of the terms the same and finding the derivatives of the other two?

But, it is hard or impossible to split up x and y that we end up differentiating the whole thing and just apply the chain rule. Onto the main point I wanted to talk about. If x and y weren't related, they'd …