Transcription
Let's learn the chain rule in 2 minutes. Look at this equation. Y = 3 x squared + 1 all to the fifth. You don't need to expand it. Multiplying it out is probably a nightmare.
But because the function is tucked inside another function, you can use the chain rule. The chain rule basically says, take the derivative of the outside function composed with the inside function and multiply it by the derivative of that inside. That's the whole thing.
In our example, the outside function is the fifth power function. The inside function is 3 x squared + 1. So, take the derivative of the outside. The derivative of the fifth power function is 5 * x to the fourth, but it's the chain rule, so we leave that inside function inside and multiply by its derivative. The derivative of 3 x squared, well, that's 3 * 2 is 6 x to the first. The derivative of 1 is 0. We won't write that. Hey, there's our derivative. You can clean up the constants multiplying them through if you like.