This week we focused on the chain rule. It's defined as fºg'(x)=f'(g(x))*g(x). This basically means that you would take the exponent of the function and bring it to the front, then multiply it by the inside of the function (which stays the same) and you raise it to the orignial exponent minus 1. Next you would multiply all of that by the derivative of the inside function. An example of this would be if f(x)=x^5, you would bring the 5 out front so it reads 5x. Next you would raise it to the original exponent minus 1 so it would be raised to the 4th power and look like this f'(x)=5x^4. Then you would multiply it by the derivative of the insdie function. The inside function is x, so the derivative of x is 1. By mutliplying it by 1, the function stays the same so f'(x)=5x^4 would be your final answer.
The chain rule can get pretty confusing the farther we move along in the unit. Right now I'm struggling with using the chain rule on 2 inside functions. However, the activity that we did in class with the whiteboards really helped me in understanding it. The part I still struggle with is simplifying!! You always end up with this really big, long, ugly mess and sometimes I get confused on what I can and can't combine. I also forget a lot that for example cos^2(x) would be the same thing as cos(x)^2. Sometimes I'll be stumped on a problem for a while until I realize that you would bring the 2 in front of the cos, then I'll beat myself up over it! It's one of those things you always tell yourself you're gonna rememeber, yet you never do.
The chain rule can get pretty confusing the farther we move along in the unit. Right now I'm struggling with using the chain rule on 2 inside functions. However, the activity that we did in class with the whiteboards really helped me in understanding it. The part I still struggle with is simplifying!! You always end up with this really big, long, ugly mess and sometimes I get confused on what I can and can't combine. I also forget a lot that for example cos^2(x) would be the same thing as cos(x)^2. Sometimes I'll be stumped on a problem for a while until I realize that you would bring the 2 in front of the cos, then I'll beat myself up over it! It's one of those things you always tell yourself you're gonna rememeber, yet you never do.