So this is the inside function, so equals and the outside function is the raising to the negative 7 that's the outside function and inside I'll make blue 2x cubed plus 3x-1. Like if I were going to plug 5 into this function I'd raise 5 to the third power multiply by 2 add 3 times 5, I'd be working on this part of the function. Usually the best way to identify inside versus outside is to think about calculating values. And so just to be absolutely clear I'm going to color code this function so that we can see what's the inside function and what's the outside function. This is just a special case of the chain rule, so let's try it out on this function h of x equals this function 2x cubed plus 3x-1 all raised to the negative 7 power. So the derivative of g of x to the n is n times g of x to the n minus 1 times the derivative of g of x. So how do you differentiate one these well we're going to use a version of the chain rule that I'm calling the general power rule. Anyway this is the chain rule I want to introduce you to what I'm calling a general power function so h of x is the general power function if it could be written as some function g of x any function raised to the nth power. We'll get into that in a second, the call with the chain rule is it's a method for differentiating composite functions like f of g of x and I've been in a habit of color coding my composite functions so that the inside part is blue and the outside part is red. Because it's so tough I've divided up the chain rule to a bunch of sort of sub-topics and I want to deal with a bunch of special cases of the chain rule, and this one is going to be called the general power rule. The chain rule is one of the toughest topics in Calculus and so don't feel bad if you're having trouble with it.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |