University:
Rice University
Course:
MATH 212 | Multivariable Calculus
Academic year:

2022
Views:

110

Pages:

1
Author:

Gurgell

Chain Rule for Derivatives. Example Problem 2 Let's take the derivative of x cubed times the sine of x squared. To do this problem, we will first look at it globally, considering both functions as a whole. The derivative is fg prime plus f prime g. So let's color code this: f and g are blue; x cubed is yellow; sin x squared is orange; and their product is purple. The chain rule allows us to take the derivative of composite functions. In this case, it's a composite function because there`s something on the inside of some parentheses that is not simply an x. A composite function: cosign times the square root of x squared plus 2x. So what we do is we take the derivative of cosign, which is cosine x squared. The inside component will stay the same, and multiply it by the derivative of the inside, which is 2x. So there you have the derivative of sine of x squared. That's 3x squared times sine x squared plus write down the derivative of f3x squared and multiply that by g(sin x), or sine x squared. And then we can clean everything up—2x cubed times 2x; well, that's 4x cubed plus 3x squared times sin x squared becomes 4x cubed plus 3x cubed times sin x cubed.